UNIT: WRITING EQUATIONS FOR LINEAR RELATIONSHIPS
he cost to produce a bag of golf tees is modeled by the function that is graphed below.Production Costs for Bags of Golf TeesWhich table shows this same function?
3
The equation is written in point-slope form. What is the y-intercept of the equation?
3/2
Which is a characteristic of the line that passes through the points (6, 10) and (12, 7)? The slope is . The slope is . The y-intercept is 7. The y-intercept is 13.
The y-intercept is 13.
Jillian and Nikki each filled their cars with gasoline. The graphs below show the amount of gas in each car and the miles driven since filling the tank.Which statement is supported by the graphs? Jillian's car holds more gasoline and gets better gas mileage. Nikki's car holds more gasoline and gets better gas mileage. Jillian's car holds more gasoline, but Nikki's car gets better gas mileage. Nikki's car holds more gasoline, but Jillian's car gets better gas mileage.
Jillian's car holds more gasoline, but Nikki's car gets better gas mileage.
What is the point-slope form of a line that has a slope of -4 and passes through point (-3, 1)?
b
Which graph represents a linear function that has a slope of 0.5 and a y-intercept of 2?
d
Which equation represents the line that passes through the points (-3, 7) and (9, -1)?
not c
Jeremy claims that if a linear function has a slope of the same steepness and the same y-intercept as the linear function in the graph, then it must be the same function. Which equation is a counterexample to Jeremy's argument?
y=-1/2x-1
A scientist created a scatter plot to represent the heights of four plants over time. Then, she found a line of best-fit to model the height in centimeters of each plant after x days. The equations of each trend line are given in the table.Trend Line EquationsPlantEquation of trend line1234According to the trend line equations, which plants are growing at the same rate per day? 1 and 2 1 and 4 2 and 3 2 and 4
1 and 4
A linear function has an x-intercept of 12 and a slope of . How does this function compare to the linear function that is represented by the table?xy It has the same slope and the same y-intercept. It has the same slope and a different y-intercept. It has the same y-intercept and a different slope. It has a different slope and a different y-intercept.
It has the same slope and a different y-intercept.
Brooke found the equation of the line passing through the points (-7, 25) and (-4, 13) in slope-intercept form as follows. What was Brooke's error? She found the incorrect slope in step 1. She mixed up the x- and y-coordinates when she plugged in the point in step 2. She found the incorrect y-intercept in step 2. She mixed up the slope and y-intercept when she wrote the equation in step 3.
She mixed up the slope and y-intercept when she wrote the equation in step 3.
Which can be the first step in finding the equation of the line that passes through the points and in slope-intercept form? Calculate . Calculate . Find that the point at which the line intersects with the line is (3, 0). Find that the point at which the line intersects with the line is (2, 2).
a
Which equation represents a line that has a slope of 1/3 and passes through point (-2, 1)?
b
Bob and Carl each rented the same kind of moving truck from EZ Move. There was a flat rental fee plus a charge per mile that the truck was driven. Bob's cost for his truck was $112.96 for 138 miles. Carl's cost for his truck was $142.78 for 209 miles. Which equation can be used to represent the cost of the rental truck? Round to the nearest hundredth if necessary.
d
The value of a collectible coin can be represented by the equation , where x represents its age in years and y represents its total value in dollars. What is the value of the coin after 19 years? $2 $23 $38 $53
not 23
Brooke found the equation of the line passing through the points (-7, 25) and (-4, 13) in slope-intercept form as follows. What was Brooke's error? She found the incorrect slope in step 1. She mixed up the x- and y-coordinates when she plugged in the point in step 2. She found the incorrect y-intercept in step 2. She mixed up the slope and y-intercept when she wrote the equation in step 3.
not She mixed up the x- and y-coordinates when she plugged in the point in step 2.
What is the equation in slope-intercept form of the linear function represented by the table?xy-6-18-1-842912
not a
Maria wrote the equation of a line that has a slope of and passes through point (3, 5). Which statement is true? The y-intercept is 4. The slope-intercept equation is . The point-slope equation is . The line also passes through the point (0, -2).
not c
What is the equation of the line passing through the points and in slope-intercept form?
not c
What is the slope-intercept form of a line that passes through points (2, 11) and (4, 17)?
not c
The table represents the total miles traveled, y, after a number of hours, x.Hours, xMiles, y2.51504.02405.53307.0420Which linear equation represents the situation?
not y=60x+480
Which table represents a linear function that has a slope of 5 and a y-intercept of 20?
table a
Emelina wrote the equation of a line in point-slope form as shown below.What is Emelina's equation in slope-intercept form? y = 3x + 2 y = 3x +10 y = 3x - 4 y = 3x - 10
y = 3x + 2
Which is the equation of a line that has a slope of 4 and passes through point (1, 6)? y = 4x - 2 y = 4x + 6 y = 4x + 2 y = 4x - 3
y = 4x + 2
The point-slope form of a line that has a slope of -2 and passes through point (5, -2) is shown below.What is the equation in slope-intercept form?
y=-2x+8
What is the equation of the linear function represented by the table?xy-514-2111845
y=-x+9
The equation is written in point-slope form. What is the equation written in slope-intercept form?
y=1/3x-9
Catherine saved some money and plans to add the same amount each week to her savings account. The table represents the number of weeks that she will save, x, and the total amount of money that she will have in her account, y. Weeks, xDollars in account, y 474686910411116 Which linear equation represents Catherine's situation?
y=6x+50
The graph shows the amount of water that remains in a barrel after it begins to leak. The variable x represents the number of days that have passed since the barrel was filled, and y represents the number of gallons of water that remain in the barrel. What is the slope of the line? -2
-2
What is the y-intercept of a line that has a slope of 3 and passes through point (-1, -7)? -10 -4 3 7
-4
Both Alex and Chris left their homes at 7:00 a.m. and walked to school. The graph shows the distances that each boy was from school as they walked.Which statement is best supported by the graph? Alex lives farther from the school than Chris lives, and Alex walked to school at a faster rate than Chris walked. Alex lives closer to the school than Chris lives, and Alex walked to school at a faster rate than Chris walked. Chris lives farther from the school than Alex lives, and Chris walked to school at a faster rate than Alex walked. Chris lives closer to the school than Alex lives, and Chris walked to school at a faster rate than Alex walked.
Chris lives farther from the school than Alex lives, and Chris walked to school at a faster rate than Alex walked.
Terri wrote the equation using slope-intercept form for the line that passes through the points (4, 6) and (-2, 3).Step 1: Step 2: Step 3: Step 4: Which best describes Terri's first error? In step 1, the slope of the line should be . In step 2, she should have substituted the point (4, 6). In step 3, she should have subtracted 4 from both sides of the equation. In step 4, the m and b values should be switched.
In step 1, the slope of the line should be 1/2
Lila wrote an equation of the cost for printing brochures, where x represents the number of brochures and yrepresents the total cost. The total cost for 35 brochures is $41.45. The total cost for 65 brochures is $55.55. Step 1: Write the ordered pairs and .Step 2: Find the slope. Step 3: Find the y-intercept to write the equation in slope intercept form. Which explains the error that Lila made? Lila made in error in Step 1 by reversing the ordered pairs. Lila made an error in Step 2 by not using the slope formula. Lila made an error in Step 3 when she did not use the x- and y-coordinates from the same ordered pair. Lila made an error in Step 3 when she did not use the distributive property correctly when multiplying.
Lila made an error in Step 3 when she did not use the x- and y-coordinates from the same ordered pair.
Which line has an equation of in slope-intercept form? a line passing through the points (1, 9) and (3, 19) a line passing through the points (2, -14) and (4, -24) a line passing through the points (1, 1) and (3, 11) a line passing through the points (2, -6) and (4, -16)
not c
The cost of a service call to fix a washing machine can be expressed by the linear function , where y represents the total cost and x represents the number of hours it takes to fix the machine. What does the y-intercept represent? the cost for each hour it takes to repair the machine the service fee for coming to look at the machine the total cost for fixing the washing machine the amount of time that it takes to arrive at the home to make the repairs
not the cost for each hour it takes to repair the machine
Which is the equation of a line that has a slope of 1 and passes through point (5, 3)? y = x - 2 y = x + 2 y = x + 3 y = x - 5
not y = x + 3
Which is the equation of a line that has a slope of 1 and passes through point (5, 3)? y = x - 2 y = x + 2 y = x + 3 y = x - 5
not y = x - 5
What is the point-slope form of a line that has a slope of -4 and passes through point (-3, 1)?
not y-(-3)=-4(x-1)
What is the equation of the line passing through the points (2, -1) and (5, -10) in slope-intercept form?
not y=-3x-5
Which is the equation of a line that has a slope of 1/2 and passes through point (2, -3)?
not y=1/2x+2
In the table below, x represents miles traveled and y represents the cost to travel by train. Miles, xCost, y28.50515.25822.001231.00Which linear equation represents the situation?
not y=2x+8.50
The cost of a service call to fix a washing machine can be expressed by the linear function , where y represents the total cost and x represents the number of hours it takes to fix the machine. What does the slope represent? the cost for each hour it takes to repair the machine the cost for coming to look at the machine the total cost for fixing the washing machine the amount of time that it takes to arrive at the home to make the repairs
the cost for each hour it takes to repair the machine
The cost of a service call to fix a washing machine can be expressed by the linear function , where y represents the total cost and x represents the number of hours it takes to fix the machine. What does the y-intercept represent? the cost for each hour it takes to repair the machine the service fee for coming to look at the machine the total cost for fixing the washing machine the amount of time that it takes to arrive at the home to make the repairs
the service fee for coming to look at the machine
Amelia and Carmen read every night. Amelia reads the same number of pages each night. So does Carmen. The table shows the number of pages that each girl has left to read after 2, 4, 5, and 7 nights of reading their books.Pages Left to ReadNightsAmeliaCarmen222522441751605150128710064Whose book has the greater number of pages? Amelia's book has 1 more page. Amelia's book has 36 more pages. Carmen's book has 7 more pages. Carmen's book has 13 more pages.
Carmen's book has 13 more pages.
A florist shop represents its first month's sales with the equation , where x represents the number of days that the shop is open and y represents the sales in dollars. The owner of the shop would like to calculate the number of days it took to reach $3,200 in sales. Which would be used to solve the problem? Substitute 3,200 for x. Add 8 and 3,200. Divide 3,192 by 168. Isolate y in the equation.
Divide 3,192 by 168.
What are the slope and the y-intercept of the linear function that is represented by the graph? The slope is , and the y-intercept is 3. The slope is , and the y-intercept is 4. The slope is , and the y-intercept is 3. The slope is , and the y-intercept is 4.
The slope is , -3/4 and the y-intercept is 3.
What is the y-intercept of a line that has a slope of and passes through point (8, 3)? 1 3 5 11
1
The libraries in four counties assess late fees for overdue videos by using linear functions. Each library charges a base amount plus a penalty for the number of weeks that the video is overdue. The equations that model the cost, y, in dollars for videos that are x weeks overdue are shown in the table.Late Fee EquationsCounty libraryLate fee functionCumberlandLincolnOceanSummitWhich two county libraries charge the same penalty per week? Cumberland and Lincoln Lincoln and Ocean Lincoln and Summit Ocean and Summit
Cumberland and Lincoln
Which is the equation of a line that has a slope of 1 and passes through point (5, 3)? y = x - 2 y = x + 2 y = x + 3 y = x - 5
y = x - 2
The equation is written in point-slope form. What is the y-intercept of the line? -13 -7 2 8
-7
What is the y-intercept of a line that has a slope of -3 and passes through point (0, -7)? -7 -3 0 4
-7
Tonya plans to join a fitness club. She researched the costs to join different clubs in her area and found that there is a linear relationship between the total cost of belonging to a club and the number of months that you are a member. Each club charges monthly dues, and some clubs require new members to also pay a one-time membership fee. The total costs of being a member for 6 months, 12 months, and 24 months at each of three clubs are shown in the table.Total Cost of Fitness Club MembershipLength of membershipClub 1Club 2Club 36 months$108$120$12612 months$216$210$25224 months$432$390$504How many of the clubs require new members to pay a one-time membership fee? 0 1 2 3
1
Sanjay consulted three electricians about upgrading the wiring in his home. Each electrician uses a linear formula that incorporates a flat base fee and an hourly rate to determine the cost of service. Those formulas are shown in the table.Repair Cost FormulasElectricianCost in y dollars for an x-hour service123Which statement is best supported by the table? Each electrician charges a different hourly rate. Each electrician charges a different base fee. All three electricians charge the same hourly rate. All three electricians charge the same base fee.
Each electrician charges a different base fee.
Which linear function has the steepest slope?
not a
The amount of money that is left in a medical savings account is expressed by the equation , where xrepresents the number of weeks and y represents the amount of money, in dollars, that is left in the account. After how many weeks will the account have $67 left in it? 10 weeks 13 weeks 15 weeks 21 weeks
13 weeks
In the table below, x represents the miles traveled and y represents the cost to travel by train. Miles, xCost, y28.50515.25822.001231.00What is the slope of this function? 0.44 0.63 2.25 22.50
2.25
A linear function can be used to estimate the decrease in snowfall measured since 1920. The decrease in the annual snowfall has been on average 0.24 inches per year. Let x represent the number of years since 1920, when the measurements began, and let y represent the annual snowfall. The initial measurement in 1920 was 48.6 inches. Using the average change and initial measurement, which is the best estimate of the annual snowfall in the 78th year after records were kept? Round to the nearest hundredth. 15.84 inches 27.72 inches 29.88 inches 67.32 inches
29.88 inches
The graph shows the number of hours that Tammy spends typing for work, x, and the amount of pay that she earns, y.What is the slope of the line? 4 6
4
In the table below, x represents miles traveled and y represents the cost to travel by train. Miles, xCost, y28.50515.25822.001231.00What is the y-intercept of this function? 2.25 4.00 6.50 17.13
4.00
A linear function has a slope of and a y-intercept of 3. How does this function compare to the linear function that is represented by the equation ? It has the same slope and the same y-intercept. It has the same slope and a different y-intercept. It has the same y-intercept and a different slope. It has a different slope and a different y-intercept.
It has the same slope and the same y-intercept.
What are the slope and the y-intercept of the linear function that is represented by the table?xy The slope is , and the y-intercept is . The slope is , and the y-intercept is . The slope is , and the y-intercept is . The slope is , and the y-intercept is .
NOT The slope is 2/5, and the y-intercept is -1/3
In 2010, Washington Township created recreational soccer programs for the spring and fall seasons. The table shows the number of participants who registered for each season during the first four years.Participation in Town Soccer ProgramsYearSpring leagueFall league2010681452011791482012901512013101154Which statement best describes the programs? Participation in the spring league is increasing more than twice as fast as participation in the fall league. Participation in the spring league is increasing at a slightly faster rate than participation in the fall league. Participation in the fall league is increasing more than twice as fast as participation in the spring league. Participation in the fall league is increasing at a slightly faster rate than participation in the spring league.
Participation in the spring league is increasing more than twice as fast as participation in the fall league.
What are the slope and the y-intercept of the linear function that is represented by the equation ? The slope is -10, and the y-intercept is -1. The slope is -10, and the y-intercept is 1. The slope is -1, and the y-intercept is -10. The slope is 1, and the y-intercept is -10.
The slope is -10, and the y-intercept is 1.
What are the slope and the y-intercept of the linear function that is represented by the table?xy-3180123660 The slope is -2, and the y-intercept is 6. The slope is -2, and the y-intercept is 12. The slope is 2, and the y-intercept is 6. The slope is 2, and the y-intercept is 12.
The slope is -2, and the y-intercept is 12.
What are the slope and the y-intercept of the linear function that is represented by the graph? The slope is , and the y-intercept is -2. The slope is , and the y-intercept is 3. The slope is , and the y-intercept is -2. The slope is , and the y-intercept is 3.
The slope is 2/3 , and the y-intercept is -2.
What are the slope and the y-intercept of the linear function that is represented by the equation ? The slope is -2, and the y-intercept is 9. The slope is 2, and they y-intercept is 9. The slope is 9, and the y-intercept is -2. The slope is 9, and the y-intercept is 2.
The slope is 9, and the y-intercept is -2.
Maria wrote the equation of a line that has a slope of and passes through point (3, 5). Which statement is true? The y-intercept is 4. The slope-intercept equation is . The point-slope equation is . The line also passes through the point (0, -2).
not The y-intercept is 4.
Which is a characteristic of the line that passes through the points (6, 10) and (12, 7)? The slope is . The slope is . The y-intercept is 7. The y-intercept is 13.
not The y-intercept is 7.
Which linear function has the same slope as the one that is represented by the table?xy0
y=-1/5x+1/10
Leon correctly found the slope and y-intercept of the line that passes through the points (9, -8) and (3, 4) as follows. What is the equation of the line in slope-intercept form?
y=-2x+10
Which linear function has the steepest slope?
y=-8x+5
Mike correctly found the slope and y-intercept of the line passing through the points (-5, -2) and (3, 14) as follows. What is the equation of the line in slope-intercept form?
y=2x+8
Which linear function has the greatest y-intercept?
y=3x+4
What is the slope-intercept form of a line that passes through points (2, 11) and (4, 17)?
y=3x+5
Which equation represents a linear function that has a slope of 4/5 and a y-intercept of -6?
y=4/5x-6
Miguel volunteers at his local food pantry and takes note of how much money is donated each day during a 10-day fundraising phone-a-thon. Below is the graph that represents the data that he collected. The slope of the line that represents the data that Miguel collected is 25, and the y-intercept is 50. What do the slope and y-intercept represent in Miguel's situation? The slope indicates that the food pantry collects $50 each day. The y-intercept indicates that the pantry began with $50 in its donation account. The slope indicates that the food pantry collects $25 each day. The y-intercept indicates that the pantry began with $25 in its donation account. The slope indicates that the food pantry collects $25 each day. The y-intercept indicates that the pantry began with $50 in its donation account. The slope indicates that the food pantry collects $50 each day. The y-intercept indicates that the pantry began with $25 in its donation account.
The slope indicates that the food pantry collects $25 each day. The y-intercept indicates that the pantry began with $50 in its donation account.
Alaina wants to decide whether her current cell phone plan is better than a package that another company offers. To compare the two plans, she plotted two lines on a graph, where y represented the total cost of one month's service and x represented the megabytes of data that she used in a month. Which part of the graph will represent the cost per megabyte of data used in each plan? The x-intercepts of the two lines The y-intercepts of the two lines. The slopes of the two lines. The coordinates of a point of intersection.
The slopes of the two lines.
Jeremy claims that if a linear function has a slope of the same steepness and the same y-intercept as the linear function in the graph, then it must be the same function. Which equation is a counterexample to Jeremy's argument?
a
Lindsay used two points, and , to find the equation of the line, y = mx + b, that passes through the points. First, she used the definition of slope and determined that the value of m is . Given this information, which expression must represent the value of b?
a
Misty correctly determined the equation of the linear function represented by the table of values below to be in slope-intercept form by using the ordered pairs (1, 7) and (2, 5). xy17253341What would she have gotten for the equation of the linear function if she had used the ordered pairs (2, 5) and (4, 1) instead?
not b
Which graph represents a linear function that has a slope of 0.5 and a y-intercept of 2?
not b
Which is the equation of a line that has a slope of and passes through point (2, -3)?
not b
Maria wrote the equation of a line that has a slope of and passes through point (3, 5). Which statement is true? The y-intercept is 4. The slope-intercept equation is . The point-slope equation is . The line also passes through the point (0, -2).
b
Which linear function has the steepest slope?
d table
Consider the linear function that is represented by the equation and the linear function that is represented by the table below. xy216426636846Which statement is correct regarding their slopes and y-intercepts? The function that is represented by the equation has a steeper slope and a greater y-intercept. The function that is represented by the equation has a steeper slope, and the function that is represented by the table has a greater y-intercept. The function that is represented by the table has a steeper slope, and the function that is represented by the equation has a greater y-intercept. The function that is represented by the table has a steeper slope and a greater y-intercept.
not The function that is represented by the equation has a steeper slope and a greater y-intercept.
Which equation represents a line that has a slope of 1/3 and passes through point (-2, 1)?
not a
Which is the equation of a line that has a slope of -2/3 and passes through point (-3, -1)?
not a
