UNIT: INPUT-OUTPUT RELATIONSHIPS

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Which linear function shows a direct variation?Graph AGraph BGraph CGraph D Graph A Graph B Graph C Graph D

graph d

What is the slope, m, and y-intercept for the line that is plotted on the grid below? m = , (0, -2) m = , (0, 4) m = 2, (0, -2) m = 2, (0, 4)

m = 2, (0, 4)

The table of values below represents a linear function and shows the amount of money in a tip jar at a dry cleaners since the dry cleaners opened for the day. How much was in the tip jar when the dry cleaners opened?Amount of Money in a Tip Jar at a Dry CleanersNumber of Hours Since Dry Cleaners Opened45678Amount of Money in Tip Jar ($)15.5018.2521.0023.7526.50 $1.75 $2.75 $4.50 $7.25

not $2.75

What is the rate of change of the function represented by the table?xy1-8.52-63-3.54-1 -2.5 -1 1 2.5

not -2.5

A teacher has a 2-gallon (32-cup) container of juice. She gives each student cup of juice. Which equation represents the amount of juice that remains, y, after x students are served?

not b

Which expression can be used to determine the slope of the linear function graphed below?

not c

Which graph represents a function with a rate of change of 0.5?

not c

Which situation is modeled by the graph? the height of a jump rope being used over time the height of an elevator over time the height of a commuter airplane over time the height of a hummingbird at a feeder

the height of a jump rope being used over time

Which linear equation has a slope of 3 and a y-intercept of -2? y = 3x + 2 y = 3x - 2 y = -2x + 3 y = -2x - 3

y = 3x - 2

A painter made the table below to show the amount of paint it takes to cover a certain amount of square feet. The amount of paint varies directly with the area of each wall.Amount of Paint and Size of WallArea of wall , x64144400Amount of paint (pints), y4925How much paint should the painter expect to use to paint a wall with an area of 256 square feet? 16 pints 32 pints 128 pints 225 pints

16 pints

Look at the graph of the linear function.The rate of change between point A and point B is 2. What is the rate of change between point C and point D? -2 2

The difference in the x-coordinates of two points is 3, and the difference in the y-coordinates of the two points is 6. What is the slope of the line that passes through the points? 2 3 6 9

Two points defining a linear function are shown in the table below. xy-14-18-10-12What is the slope of the function? 2 6

3/2

The table of values below represents a linear function and shows the height of a tree since it was transplanted. What was the height of the tree when it was transplanted?Height of a Tree Since It Was TransplantedYears Since the Tree Was Transplanted44.555.56Height (feet)1213141516 1 foot 2 feet 4 feet 8 feet

4ft

A line passes through the points (2, -2) and (-6, 2). The point (a, -4) is also on the line. What is the value of a? -6 -1 1 6

Look at the graph. To find the rate of change of the function, Kevin did the following: What was Kevin's mistake? He incorrectly chose (-1, 2.5) as a point on the graph. He incorrectly chose (0, 2) as a point on the graph. He mixed up the numerator and the denominator of the fraction. He subtracted -1 from 0 when he should have added -1 to 0.

He mixed up the numerator and the denominator of the fraction.

Asha found that a vertical line intersects the graph of at two points. What can Asha conclude about ? It is a function of x but not a relation. It is a relation but not a function of x. It is both a function of x and a relation. It is neither a function of x nor a relation.

It is a relation but not a function of x.

Kelsey graphed the equation y = 3x + 1 as shown below.Which describes Kelsey's error? Kelsey graphed the y-intercept on the x-axis. Kelsey graphed -3 instead of 3 as the y-intercept. Kelsey graphed the slope as up 1 right 1 instead of up 1 left 1. Kelsey graphed the slope as the y-intercept and the y-intercept as the slope.

Kelsey graphed the slope as the y-intercept and the y-intercept as the slope.

Which statement correctly compares the constants of variation for the graph and the equation below? The graph has a greater constant of variation. The equation has a greater constant of variation. The constant of variation is the same for the graph and the equation. The constant of variation cannot be compared because the equation is nonproportional.

The equation has a greater constant of variation.

A person weighs a different amount on other surfaces in space than they do on Earth because the gravitational pull of each surface is different than that of Earth. The table and graph show the weights of objects on Earth, Mars, and the Moon.Weight on Earth and MarsWeight on Earth, e90 pounds120 pounds160 poundsWeight on Mars, a36 pounds48 pounds64 poundsWeight on Earth and MoonIf a person weighs 240 pounds on Earth, what would be the difference in weight of the same person on Mars and on the Moon (based on the table and graph)? The person weighs 56 pounds more on Mars than on the Moon. The person weighs 56 pounds more on the Moon than on Mars. The person weighs 560 pounds more on Mars than on the Moon. The person weighs 560 pounds more on the Moon than on Mars.

The person weighs 56 pounds more on Mars than on the Moon.

Which statement correctly describes the slope of the linear function that is represented by the data in the table?xy8-88-4808488 The slope is positive. The slope is negative. The slope is zero. There is no slope.

There is no slope.

The graph below represents the total shipping cost of x items for four different companies. Shipping ChargesWhich list places the companies in order from the steepest slope to the least steep slope? W, Z, U, Y U, Y, W, Z W, Z, Y, U U, Y, Z, W

W, Z, U, Y

Nate went on a trip, and he used a table of values to repeatedly record the time he had been traveling and the distance from his starting point. The function represented by the table of values is linear, and the rate of change is 50 miles per hour. Which of these statements is correct? With any pair of values for time and distance, it is possible for Nate to determine the initial value by repeatedly adding 50, if necessary. With any pair of values for time and distance, it is possible for Nate to determine the initial value by repeatedly subtracting 50, if necessary. With any pair of values for time and distance, it is possible for Nate to determine the initial value by repeatedly multiplying by 50, if necessary. With any pair of values for time and distance, it is possible for Nate to determine the initial value by repeatedly dividing by 50, if necessary.

With any pair of values for time and distance, it is possible for Nate to determine the initial value by repeatedly subtracting 50, if necessary.

Jada fills the bathtub before taking a bath and then allows the water to drain when she is done. The graph below models the number of gallons of water, y, in the bathtub over time, t, in minutes. Is the number of gallons of water in the bathtub a function of time? Yes because each t value is paired with exactly one number of gallons. Yes because the number of gallons is bounded between y = 0 and y = 36. No because each number of gallons is paired with more than one t value. No because from t = 5 to t = 20 the number of gallons of water is constant.

Yes because each t value is paired with exactly one number of gallons.

A line has a slope of and passes through the point (-3, 8). What is the equation of the line?

A line passes through the point (4, -6) and has a slope of . Which is the equation of the line?

A line passes through the points (-1, 10) and (3, 2). Which shows the graph of this line?

A line passes through the points (-3, 7) and (6, 4). Which shows the graph of this line?

A line passes through the points (-5, 2) and (10, -1). Which is the equation of the line? y = -5x - 23 y = 5x + 27

A line passes through the points (1, 4) and (3, -4). Which is the equation of the line? y = -2x + 6 y = 2x + 2

A line is defined by the equation . Which shows the graph of this line?

Ava wrote the expression to determine the slope of a line. Which table might represent Ava's line?

Lorena calculated the slope of the linear function that is represented by the table of values as shown.xy-1015-827-639-451-263What did she do wrong? She used the wrong formula for slope. She used the wrong points to determine the slope. She made a mistake when she subtracted from . She made a mistake when she subtracted from .

The linear function that is represented by which table has the same slope as the graph?

Which is a qualitative graph?

The linear function graphed below represents Brenda's monthly cell phone bill based on the number of hours she uses. What is her hourly rate? $12 per hour $15 per hour $27 per hour $39 per hour

$12 per hour

The table of values below represents a linear function and shows the amount of money in Juanita's savings account since she began her part-time job. What is her monthly rate of savings?Amount in Juanita's Savings AccountNumber of Months Working at Part-Time Job02468Amount in Savings Account (in dollars)$36$60$84$108$132 $12 per month $18 per month $24 per month $36 per month

$12 per month

A horizontal line passes through the point (5, -1). Which point is also on this line? (0, 0) (-1, 5) (5, -4) (-2, -1)

(-2, -1)

Maricella plots two ordered pairs on the grid below. The line segment is extended to cross both axes. What is the location of the y-intercept on the line? (0, -22) (0, -10) (0, -5) (0, 5)

(0, -10)

A line passes through the point (-7, 5) and has a slope of . Which is another point that the line passes through? (-13, 9) (-9, 13) (9, 13) (13, 9)

(9, 13)

What is the rate of change of the function? -2 2

-2

The table represents a linear function. The rate of change between the points (-5, 10) and (-4, 5) is -5. What is the rate of change between the points (-3, 0) and (-2, -5)?xy-510-45-30-2-5 -5 5

-5

A line passes through the point (4, -2) and has a slope of . What is the value of a if the point (-4, a) is also on the line? -6 -5 5 6

-6

Sue graphed the formula for converting temperatures from Fahrenheit to Celsius.If the temperature is 50 degrees Fahrenheit, what is the temperature in Celsius? 5 degrees Celsius 10 degrees Celsius 15 degrees Celsius 20 degrees Celsius

10 degrees Celsius

The speed of an object in space is shown in the graph.What is the slope of the line? 10 15 20 25

The ordered pairs in the table below represent a linear function.xy6298What is the slope of the function? 2 4

What is the slope of the line represented by the values in the table?xy10142-230782034

A botanist uses the representations below to show the heights in inches, h, of different plants over a period of time, t.Plant ATime in weeks, t6080100120Height in inches, h90120150180Plant BIf the growth patterns continue, how much taller is the tallest plant than the shortest plant at 120 weeks of growth? 180 inches 200 inches 270 inches 280 inches

200 inches

The table of values below represents a linear function and shows Marco's progress as he is pumping gas into his car. What is the output for the initial value?Gas in Marco's CarSeconds Spent Pumping Gas012243648Gallons of Gas in Car357911 0 gallons 2 gallons 3 gallons 6 gallons

3 gallons

Max is painting a fence.The table shows the number of square feet he painted after various numbers of minutes. What is the rate of change?Amount of Fence Max PaintedMinutesSquare Feet Painted13.527310.5414517.5 -3.5 -1 1 3.5

3.5

The table below shows the number of color pages a printer prints out over a period of time.Printed Pages in ColorTime (min), x26818Number of pages, y391227What is the constant of variation? 2 3

3/2

Given that y varies directly with x in the table below, what is the value of y if the value of x is 7?x24610y12243660 37 42 48 54

The linear function graphed below represents the height of a stalk of corn since a farmer began using a new fertilizer. What is the initial value? 0 feet 1 foot 4 feet 6 feet

4ft

Xavier is attempting to recreate a problem his teacher showed him in class. To do so, he creates the table below.xy132?He remembers that the slope of the line through the ordered pairs in the table was 4. What is the missing y-value in the table? 5 7 8 12

Four students drew graphs of a linear function. Which student drew a line with a slope of 3?AnaliseBenitoCharlieDariya Analise Benito Charlie Dariya

Benito

Fun Zone offers four party packages. The prices for each package are $50 more on weekends than they are on weekdays, as shown in the table below.Party Package RatesPackage numberWeekend or weekdayPrice1Weekend$1601Weekday$1102Weekend$1802Weekday$1303Weekend$2303Weekday$1804Weekend$3004Weekday$250Which statement best describes the relation (package number, price)? It is a function because there is a price given for every package. It is a function because weekend packages are always $50 more than weekday packages. It is not a function because each package number has two different prices. It is not a function because there are two different packages available for $180.

It is not a function because each package number has two different prices.

Mrs. Jacobson asked her students to write a word problem that describes the graph below.Which word problem accurately describes the graph? Jamie has $8, and she pays $2 per day to ride the bus. Melinda has $4 and earns $2 allowance per day doing chores. Carrina has $8, and she earns $2 per day babysitting. Louise has $4, and she pays $2 per day for school lunch.

Jamie has $8, and she pays $2 per day to ride the bus.

Both Andrew and Karleigh recorded the distance they ran in x minutes on treadmills.AndrewKarleighAndrew and Karleigh each run for 1 hour. Which statement explains who ran a greater distance? Andrew ran a greater distance. The slope of the line described by the data in his table increased at a rate of mile per minute compared to Karleigh's mile per minute. Karleigh ran a greater distance. The slope of the line described by the data in her table increased at a rate of mile per minute compared to Andrew's mile per minute. Karleigh ran a greater distance. The slope of the line described by the data in her table increased at a rate of mile per minute compared to Andrew's mile per minute. Andrew ran a greater distance. The slope of the line described by the data in his table increased at a rate of mile per minute compared to Karleigh's mile per minute.

Karleigh ran a greater distance. The slope of the line described by the data in her table increased at a rate of mile per minute compared to Andrew's mile per minute.

The slope of a line is 2. The y-intercept of the line is -6. Which statements accurately describe how to graph the function? Locate the ordered pair (0, -6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points. Locate the ordered pair (0, -6). From that point on the graph, move up 2, left 1 to locate the next ordered pair on the line. Draw a line through the two points. Locate the ordered pair (-6, 0). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points. Locate the ordered pair (-6, 0). From that point on the graph, move up 2, left 1 to locate the next ordered pair on the line. Draw a line through the two points.

Locate the ordered pair (0, -6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.

Which statements accurately describe how to determine the y-intercept and the slope from the graph below? To find the y-intercept, begin at the origin and move horizontally to the graphed line. To find the slope, use two ordered pairs on the line and substitute into the equation . To find the y-intercept, begin at the origin and move horizontally to the graphed line. To find the slope, use two ordered pairs on the line and substitute into the equation . To find the y-intercept, begin at the origin and move vertically to the graphed line. To find the slope, use two ordered pairs on the line and substitute into the equation . To find the y-intercept, begin at the origin and move vertically to the graphed line. To find the slope, use two ordered pairs on the line and substitute into the equation .

NOT D

Lydia writes the equation below with a missing value.She puts a value in the box and says that the equation represents a direct variation. Which explains whether the equation could represent a direct variation? If she puts 0 in the box she would have a direct variation. If she puts 5 in the box she would have a direct variation. The equation is not of the form , so it cannot represent a direct variation. The equation has a minus sign, so it cannot represent a direct variation.

NOT The equation is not of the form , so it cannot represent a direct variation.

Which explains whether or not the graph represents a direct variation? The graph has a constant of variation of 3, so it represents a direct variation. The graph has a slope of 3, so it represents a direct variation. The graph has a positive slope, so it does not represent a direct variation. The graph does not begin at the origin, so it does not represent a direct variation.

NOT The graph has a slope of 3, so it represents a direct variation.

A teacher has a 2-gallon (32-cup) container of juice. She gives each student cup of juice. Which equation represents the amount of juice that remains, y, after x students are served?

NOT d

The graph has a constant of variation of 3, so it represents a direct variation.

How does the graph change between point A and point C? The graph increases, then decreases. The graph decreases, then remains constant. The graph decreases, then increases. The graph increases, then remains constant.

The graph increases, then remains constant.

How does this graph change between point D and point G? The graph increases. The graph decreases. The graph increases, then decreases. The graph remains constant.

The graph increases.

The linear function graphed below represents Tim's age in the years since he was married. Which of these statements is correct? The initial value is 22, and the rate of change is 1. The initial value is 22, and the rate of change is 15. The initial value is 32, and the rate of change is 1. The initial value is 32, and the rate of change is 15.

The initial value is 32, and the rate of change is 1.

The table below shows how much Joe earns, y, after working x hours. Joe's EarningsHours workedMoney earned4$3010$7512$9022$165The relationship between money earned and hours worked is linear. Joe computes the slope between (4, 30) and (12, 90), then computes the slope between (4, 30) and (10, 75). How do the two slopes compare? The slope between (4, 30) and (12, 90) is greater because the ordered pairs are farther apart on the x-axis. The slope between (4, 30) and (12, 90) is greater because the ordered pairs are farther apart on the y-axis. The slope between (4, 30) and (12, 90) and between (4, 30) and (10, 75) is the same. The slope between (4, 30) and (12, 90) is less because 4 is a factor of 12 and 30 is a factor of 90.

The slope between (4, 30) and (12, 90) and between (4, 30) and (10, 75) is the same.

In the table, x represents minutes, and y represents the altitude of an airplane. Altitude of an AirplaneMinutes, xAltitude in feet, y1522,5002020,0002517,5003015,000Which statement is correct about the slope of the linear function that the table represents? The slope is positive because as the minutes decrease, the altitude increases. The slope is positive because as the minutes increase, the altitude increases. The slope is negative because as the minutes decrease, the altitude decreases. The slope is negative because as the minutes increase, the altitude decreases.

The slope is negative because as the minutes increase, the altitude decreases.

Which explains whether or not the values in the table represent a direct variation?x461020y11.52.55 The table represents a direct variation because the values are proportional. The table represents a direct variation because the values are nonproportional. The table does not represent a direct variation because the values are proportional. The table does not represent a direct variation because the values are nonproportional.

The table represents a direct variation because the values are proportional.

Is the function in the graph non-linear? Yes, because it has a constant rate of change. Yes, because it does not have a constant rate of change. No, because it has a constant rate of change. No, because it does not have a constant rate of change.

Yes, because it does not have a constant rate of change.

Eric earns a weekly salary and a commission on each item that he sells. The equation y = 10x + 50 represents the amount of money that Eric earns weekly. Bailey earns a greater weekly salary than Eric but the same commission rate. Which graph could represent the amount of money that Bailey earns weekly, y, based on the number of items sold, x?

The equation represents the gallons of gasoline that remain in Michelle's car after she drives x miles. Which graph represents this equation?

The length of a spring varies directly with the mass of an object that is attached to it. When a 30-gram object is attached, the spring stretches 9 centimeters. Which equation relates the mass of the object, m, and the length of the spring, s?

The number of milligrams of a certain medicine a veterinarian gives to a dog varies directly with the weight of the dog. If the veterinarian gives a 30-pound dog milligram of the medicine, which equation relates the weight, w, and the dosage, d?

The table represents the cost of flowers at the Tigerlily Flower Shop.Cost of FlowersQuantityPrice1$2.002$3.503$5.004$6.505$8.006$9.00Which graph is the best interpretation of this table?

The table shows the number of minutes Jalen talks on his mobile phone and the cost of the phone calls.Jalen's Mobile Phone CostNumber of minutes, x150220250275Cost, y$7.50$11.00$12.50$13.75If the cost varies directly with the number of minutes Jalen talks on the phone, which equation represents the variation?

What is the equation of a line through the points (0, 9) and (3, 0)? because ; y = -3x + 9 because ; y = -3x + 3 because ; because ;

Which expression can be used to determine the slope of the linear function represented in the table?xy0549

Which graph or equation represents a nonproportional relationship?ABCy 0.375xD A B C D

Which table represents the graph below?

William is in the middle of swimming in a ten-mile race. He swims at a steady speed, and then slows down, stops to eat, swims faster to get back in the race, and returns to a steady speed. He later stops for water, and then again swims faster to get back in the race. Which graph best represents the situation?

A sand dune stands 5 feet above sea level. The hill is eroding at a rate of 1 foot per 20 years. Let y represent the height of the sand dune after x years. Which equation represents the situation?

Which graph represents a linear function?

Marisol attempted to determine the slope of a line based on the two points shown in the table below.xy-14310Step 1: (-1, 4) and (3, 10)Step 2: Step 3: Which statement best explains Marisol's error? Marisol computed . Marisol computed . Marisol computed . Marisol computed .

Which expression can be used to determine the slope of the line that passes through the points (-7, 3) and (1, -9)?

Which is the graph of the linear function that is represented by the equation ?

Which of these tables represents a non-linear function?

A line passes through the points (-2, -8) and (-4, -8). Which shows the graph of this line?

At breakfast, a restaurant charges $2 for the first cup of orange juice and then $1 for each refill. Which graph represents this situation?

Which graph represents a function with a rate of change of 0.5?

Which representation represents a proportional relationship?Ax2468y681012BCDx471215y8142430 A B C D

Four students graphed one linear function each.RhettCameronEllisBradenWhich student graphed a linear function with a y-intercept at -4? Rhett Cameron Ellis

ellis

Four students graphed one linear function each.RhettCameronEllisBradenWhich student graphed a linear function with a y-intercept at -4? Rhett Cameron Ellis Braden

ellis

not $2.75

The linear function graphed below represents the value of a comic book since Lucy purchased it. What was the value of the comic book when Lucy bought it? $10 $15 $25 $40

not $40

Caleb made the table below to show the number of hours he works and the amounts he earns over a four-week period.Caleb's EarningsHours12151821Earnings(in dollars)140170200230Which describes whether the relationship between the earnings and the number of hours represents a direct variation? He earns 20 more than 10 times the number of hours he works each week, so the earnings vary directly with the hours. The earnings increase by 30 for every increase of 3 hours, so the earnings vary directly with the hours. The ratios of earnings to hours are not the same each week, so the earnings do not vary directly with the hours. The earnings increase at a steady rate, so the earnings do not vary directly with the hours.

not The earnings increase by 30 for every increase of 3 hours, so the earnings vary directly with the hours.

not d

A veterinarian knows that a 50-pound dog gets 0.5 milligram of a certain medicine, and that the number of milligrams, m, varies directly with the weight of the dog, w. The vet uses these steps to find the amount of medicine to give a 10-pound dog.Step 1Find the constant of variation.Step 2Write the direct variation equation.Step 3Substitute 10 into the equation to find the dosage for a 10-pound dog.Step 4Solve for w.The 10-pound dog needs 1000 milligrams.In which step did the veterinarian make the first error? Step 1 Step 2 Step 3 Step 4

step 3

Which table represents a direct variation?Table Ax46810y791113Table Bx46810y12182430Table Cx46810y1357Table Dx46810y3333 Table A Table B Table C Table D

table b

The situation that is best modeled by a discrete graph is the daily records of the distance of each hotel from home during a cross-country trip. the height of a wave over time. the speed of a motorcycle over the distance it travels. the body temperature of an athlete during a workout.

the daily records of the distance of each hotel from home during a cross-country trip.

Which equation represents a line with an undefined slope? y = x y = -x y = 0 x = 0

x = 0

The linear equation when b = 5 and m = -2 is y = 5x - 2. y = 5x + 2. y = -2x - 5. y = -2x + 5.

y = -2x + 5

Sanjay said that if a line has a slope of zero, then it never touches the x-axis. Which line proves that his statement is incorrect? x = 0 y = 0 x = 1 y = 1

y = 0

The estimated total cost, y, of a child's toy is partially based on the number of batteries used, x. The cost of one battery is $0.75. The toy itself costs $12. Which equation represents the situation? y = 12x + 0.75 y = 0.75x + 12 y = 12x - 0.75 y = 0.75x - 12

y = 0.75x + 12

Adriana writes the equation y = 2x + 4 to represent a line on a graph. Henry writes an equation that has a y-intercept that is 1 unit lower on the graph but has the same slope as Adriana's line. Which is Henry's equation? y = x + 4 y = 3x + 4 y = 2x + 3 y = 2x + 5

y = 2x + 3

Jordana drew the function below. Which statement correctly explains whether or not her function is linear? It is linear because it has a constant rate of change. It is linear because it does not have a constant rate of change. It is not linear because it has a constant rate of change. It is not linear because it does not have a constant rate of change.

It is not linear because it does not have a constant rate of change.

Removing which point from the coordinate plane would make the graph a function of x? (-4, 3) (-2, 1) (0, 4) (1, 1)

(-2, 1)

The table of values shown below represents a linear function. Which of these points could also be an ordered pair in the table, and why?x036912y37111519 (18, 27), because the rate of change of the function is (18, 27), because the rate of change of the function is (27, 18), because the rate of change of the function is (27, 18), because the rate of change of the function is Submitted

(18, 27), because the rate of change of the function is

Removing which ordered pair from the table would make the relation a function of x? xy1747224139 (1, 7) (2, 2) (3, 9) (4, 1)

(4, 1)

The table below lists some of the characteristics of the houses on Katrina's street.Characteristics of Homes For Sale on Katrina's StreetBedroomsAcres of landSale priceAppraised valueProperty tax20.17$230,000$200,000$1,22020.20$210,000$220,000$1,23230.20$275,000$250,000$1,40040.24$275,000$275,000$1,54040.52$360,000$310,000$1,73640.75$350,000$320,000$1,79251.23$375,000$350,000$1,960Which relationship describes a function? (bedrooms, sale price) (acres of land, appraised value) (sale price, bedrooms) (appraised value, property tax)

(appraised value, property tax)

If the relationships below are given in the form (input, output), which pairing always describes a function? (number of doors in a car, number of cup holders in the car) (height of a building in feet, height of the building in inches) (beverage charge on a bill, total meal charge on the bill) (distance from home during a trip, time elapsed during the trip)

(height of a building in feet, height of the building in inches)

What is the rate of change of the function represented by the table?xy15253545 0 1 4 5

The table of values below represents a linear function and shows the number of miles on the odometer of Brian's moped since he started riding it. What is Brian's speed?Miles on the Odometer of Brian's MopedNumber of Minutes Brian Has Been Riding Moped0481216Number of Miles Traveled3.254.255.256.257.25 0.25 miles per minute 1 mile per minute 3.25 miles per minute 4 miles per minute

0.25 miles per minute

Corinne and Aretha are having a 26-mile race. Corinne gave Aretha a head start by letting her begin 3.5 miles in front of the start line. Their distances past the start line as the race has progressed can be represented by linear functions and are shown in the table and graph below. How many minutes after the start of the race will Corinne catch Aretha?Corinne's Distance Past the Start LineTime (minutes)1020304050Distance (miles)1.252.53.755.06.25 140 minutes 180 minutes 208 minutes 225 minutes

140 minutes

During 30 minutes on the treadmill, LaToya burned 20 calories per minute. What is the rate of change of the function that represents this situation? 10 calories per minute 20 calories per minute 30 calories per minute 50 calories per minute

20 calories per minute

Hideki is draining a 45-gallon aquarium at a rate of 15 gallons per minute. What is the initial value of the linear function that represents this situation? 15 gallons 30 gallons 45 gallons 60 gallons

45 gallons

Mia records the distance traveled in x minutes in the table below, while Alexa uses a graph to record her distance traveled over the same time period. Alexa's GraphMia's TableBased on the data on the graph and in the table, which statement gives an accurate comparison? Alexa traveled at a faster rate because the slope of her line is , which is greater than the slope of the line described by the data in Mia's table. Alexa traveled at a faster rate because the slope of her line is , which is greater than the slope of the line described by the data in Mia's table. Mia traveled at a faster rate because the slope of the line described by the data in her table is , which is greater than the slope of the line on Alexa's graph. Mia traveled at a faster rate because the slope of the line described by the data in her table is , which is greater than the slope of the line on Alexa's graph.

Alexa traveled at a faster rate because the slope of her line is , which is greater than the slope of the line described by the data in Mia's table.

Antonio and Candice had a race. Their distances past a particular landmark as the race progressed can be represented by linear functions and are shown in the table of values and graph below. Which statement is true regarding Antonio and Candice's race?Antonio's Distance Past the LandmarkTime (seconds)812162024Distance (meters)2941536577 Antonio had a head start of 1 meter. Antonio had a head start of 3 meters. Candice had a head start of 1 meter. Candice had a head start of 3 meters.

Antonio had a head start of 3 meters.

The chart below lists the original and sale prices of items at a clothing store.Clothing PricesOriginal priceSale price$7.99$5.59$10.99$7.69$12.99$9.09$15.99$11.19$24.99$17.49$29.99$20.99Which statement best describes why the sale price is a function of the original price? As the original price increases, the sale price also increases. The sale price is always less than the original price. For every original price, there is exactly one sale price. The sales price is never less than zero.

For every original price, there is exactly one sale price.

Richard and Gloria ran a 10-kilometer race. Gloria gave Richard a head start by letting him begin 2.2 kilometers in front of the start line. The distances of Richard and Gloria past the start line as the race progressed can be represented by linear functions and are shown in the table of values and graph below. Whose time was faster, and by how much?Richard's Distance Past the Start LineTime (minutes)510152025Distance (kilometers)2.83.44.04.65.2 Gloria's time was 0.5 minutes faster. Richard's time was 0.5 minutes faster. Gloria's time was 2.5 minutes faster. Richard's time was 2.5 minutes faster.

Gloria's time was 2.5 minutes faster.

Look at the graph. Leslie analyzed the graph to determine if the function it represents is linear or non-linear. First she found three points on the graph to be (-1, -4), (0, -3), and (2, 5). Next, she determined the rate of change between the points (-1, -4) and (0, -3) to be and the rate of change between the points (0, -3) and (2, 5) to be . Finally, she concluded that since the rate of change is not constant, the function must be linear. Why is Leslie wrong? The points (-1, -4), (0, -3), and (2, 5) are not all on the graph. The expressions and both equal 1. She miscalculated the rates of change. Her conclusion is wrong. If the rate of change is not constant, then the function cannot be linear.

Her conclusion is wrong. If the rate of change is not constant, then the function cannot be linear.

A line passes through the points (7, 10) and (7, 20). Which statement is true about the line? It has a slope of zero because in the formula is zero, and the numerator of a fraction cannot be zero. It has a slope of zero because in the formula is zero, and the denominator of a fraction cannot be zero. It has no slope because in the formula is zero, and the numerator of a fraction cannot be zero. It has no slope because in the formula is zero, and the denominator of a fraction cannot be zero.

It has no slope because in the formula is zero, and the denominator of a fraction cannot be zero.

At 5:00 p.m., Antonio turned on the oven. While the oven preheated, the temperature in the oven increased from 72°F to 400°F over a 10-minute period. The oven remained at 400°F for 45 minutes until Antonio turned it off. It took 60 minutes for the temperature in the oven to cool, returning to 72°F at 6:55 p.m. Which statement best explains whether or not the temperature in the oven is a function of the time? It is a function because at any given time the oven was exactly one temperature. It is a function because the oven temperature was the same at different times. It is not a function because at any given time the oven was exactly one temperature. It is not a function because the oven temperature was the same at different times.

It is a function because at any given time the oven was exactly one temperature.

The temperature in degrees Celsius, c, can be converted to degrees Fahrenheit, f, using the equation . Which statement best describes if the relation (c, f) is a function? It is a function because -40°C is paired with -40°F. It is a function because every Celsius temperature is associated with only one Fahrenheit temperature. It is not a function because 0°C is not paired with 0°F. It is not a function because some Celsius temperatures cannot be associated with a Fahrenheit temperature.

It is a function because every Celsius temperature is associated with only one Fahrenheit temperature.

On the way to her babysitting job, Mary rode her bike for the first mile. She stopped at a traffic light and waited a few minutes for the traffic light to turn green. She then walked her bike across the street and up a short steep hill. Finally, she rode the bike at a constant speed for one more mile. If Mary created a graph of her time and distance, which statement describes the part of her graph that would show no change in distance? Mary used her bike to ride the first mile. Mary stopped and waited for the traffic light to turn green. Mary walked her bike across the avenue and up a short hill. Mary rode her bike at a constant speed for one mile.

Mary stopped and waited for the traffic light to turn green.

Which statement is a correct interpretation of the vertical line test? If only one vertical line intersects the graph at exactly one point, the graph represents a function. If only one vertical line intersects the graph at exactly one point, the graph does not represent a function. If any vertical line can intersect the graph at more than one point, the graph represents a function. If any vertical line can intersect the graph at more than one point, the graph does not represent a function.

NOT If any vertical line can intersect the graph at more than one point, the graph represents a function.

The graph below displays the wrist circumferences and heights of six students in Alyssa's classroom. Is the height of these students a function of their wrist circumference? Yes because as wrist circumference increases height also increases. Yes because a line can be fit to these data to predict other pairings. No because the height of 151 cm is paired with two wrist circumferences. No because the wrist circumference of 16 cm is paired with two heights.

No because the wrist circumference of 16 cm is paired with two heights.

Eric received a gift card worth $25 as a birthday present. He is spending $2.50 per day using the gift card, as shown in the graph below. Which statement is true about the linear function that represents his gift card spending? The initial value is the amount on the gift card before Eric starts using it. The initial value is the amount on the gift card after Eric finishes using it. The rate of change is the amount on the gift card before Eric starts using it. The rate of change is the amount on the gift card after Eric finishes using it.

The initial value is the amount on the gift card before Eric starts using it.

A computer had 2 gigabytes of data stored on it when Jackie bought it, and she is storing an additional 3.5 gigabytes per year, as shown in the table below. Which of these statements is correct about the linear function that represents this situation?Amount of Data Stored on Jackie's ComputerTime (year)01234Gigabytes of Data22 + 3.5 = 5.55.5 + 3.5 = 99 + 3.5 = 12.512.5 + 3.5 = 16 The initial value represents the 2 gigabytes of data stored on the computer when Jackie bought it, and the rate of change represents the 3.5 gigabytes per year that Jackie is storing. The initial value represents the 2 gigabytes per year that Jackie is storing, and the rate of change represents the 3.5 gigabytes of data stored on the computer when Jackie bought it. The initial value represents the 3.5 gigabytes of data stored on the computer when Jackie bought it, and the rate of change represents the 2 gigabytes per year that Jackie is storing. The initial value represents the 3.5 gigabytes per year that Jackie is storing, and the rate of change represents the 2 gigabytes of data stored on the computer when Jackie bought it.

The initial value represents the 2 gigabytes of data stored on the computer when Jackie bought it, and the rate of change represents the 3.5 gigabytes per year that Jackie is storing.

Isaac and Sakura are both doing a science experiment where they are measuring the temperature of a liquid over time. Graphs that represent each of their data are shown below.Which statement is correct? The slope of the graph that represents Isaac's data is positive, and the slope of the graph that represents Sakura's data is positive. The slope of the graph that represents Isaac's data is positive, and the slope of the graph that represents Sakura's data is negative. The slope of the graph that represents Isaac's data is negative, and the slope of the graph that represents Sakura's data is positive. The slope of the graph that represents Isaac's data is negative, and the slope of the graph that represents Sakura's data is negative.

The slope of the graph that represents Isaac's data is negative, and the slope of the graph that represents Sakura's data is positive.

A company has determined that its weekly profit is a function of the number of items that it sells. Which equation could represent the weekly profit in thousands of dollars, y, when the company sells x items?

Which graph has a rate of change of zero?

Which graph is a function of x?

Which of these tables represents a linear function?

On the way to the mall Miguel rides his skateboard to get to the bus stop. He then waits a few minutes for the bus to come, then rides the bus to the mall. He gets off the bus when it stops at the mall and walks across the parking lot to the closest entrance. Which graph correctly models his travel time and distance?

The table below represents the number of math problems Jana completed as a function of the number of minutes since she began doing her homework. Does this situation represent a linear or non-linear function, and why?Jana's Math Homework ProgressMinutesMath Problems Completed1327312416519 It represents a linear function because there is a constant rate of change. It represents a linear function because there is not a constant rate of change. It represents a non-linear function because there is a constant rate of change. It represents a non-linear function because there is not a constant rate of change.

Carol is cross-country skiing. The table shows the distance she traveled after various numbers of minutes. What is the rate of change?Distance Carol Traveled while Cross-Country SkiingMinutesDistance Traveled (miles)23456

not 1/6

not It is both a function of x and a relation.

not It is linear because it has a constant rate of change.

Is the function represented by the table linear?xy10-61111261312 Yes, because it has a constant rate of change. Yes, because it does not have a constant rate of change. No, because it has a constant rate of change. No, because it does not have a constant rate of change.

not No, because it has a constant rate of change.

Is the function represented by the table non-linear?xy6472809-2 Yes, because it has a constant rate of change. Yes, because it does not have a constant rate of change. No, because it has a constant rate of change. No, because it does not have a constant rate of change.

not Yes, because it has a constant rate of change.

Juno is taking a taxi. The table represents a linear function and shows the amount she owed after various numbers of miles traveled. Is the rate of change 2.25?Amount Juno Owed for a TaxiMilesAmount Owed (dollars)12.524.753749.25511.5 Yes, because the amount owed changes by 1 every time the miles change by 2.25. Yes, because the amount owed changes by 2.25 every time the miles change by 1. No, because the amount owed does not change by 1 every time the miles change by 2.25. No, because the amount owed does not change by 2.25 every time the miles change by 1.

not Yes, because the amount owed changes by 1 every time the miles change by 2.25.

UNIT: INPUT-OUTPUT RELATIONSHIPS

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