Writing and Graphing Equations in Two Variables

Berto has $12 to put gas in his car. If gas costs $3.75 per gallon, which ordered pair relating number of gallons of gas, x, to the total cost of the gas, y, includes the greatest amount of gas Berto can buy?

(3.2 , 12)

Jayne stopped to get gas before going on a road trip. The tank already had 4 gallons of gas in it. Which equation relates the total amount of gasoline in the tank, y, to the number of gallons that she put in the tank, x? y=4+x y = x − 4 y = 4 · x y = x ÷ 4

y=4+x

Otto used 5.5 cups of whole wheat flour and x cups of white flour in the recipe. What is the equation that can be used to find the value of y, the total amount of flour that Otto used in the recipe, and what are the constraints on the values of x and y? y=5.5x; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 5. y=5.5x; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 5.5. y=x+5.5; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 5. y=x+5.5; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 5.5.

y=x+5.5; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 5.5.

A tub filled with 50 quarts of water empties at a rate of 2.5 quarts per minute. Let w = quarts of water left in the tub and t = time in minutes. Choose the correct answers. Which equation models the relationship? Is there a viable solution when time is 30 minutes?

✔ w = 50 - 2.5t ✔ No, the tub will be empty by then.

The graph below shows the amount of money left in the school's desk fund, f, after d desks have been purchased. For each new desk that is purchased, by how much does the amount of money left in the school's desk fund decrease? $110 $135 $165 $190

$110

Juan spent 10 minutes on his history homework and 3 minutes per question on his math homework. Which graph shows the total homework time, t, related to the number of math questions, q?

A

The graph shows the relationship between pounds of grapes, g, and their cost, c. Use the graph to complete the statements. For every dollar you spend, you can get pounds of grapes. For each pound of grapes, you would need $.

0.5 2

Each Friday, the school prints 400 copies of the school newsletter. The equation c = 400w models the relationship between the number of weeks and the total number of copies of the newsletters printed. What is true of the graph of this scenario?A viable point on the graph is ________The values of w must be________

(8, 3,200)any whole number

The graph shows the relationship between the number of minutes Maria spent jogging on a treadmill and the distance she jogged. What was her speed? 0.1 mile per minute 0.5 mile per minute 5 miles per minute 10 miles per minute

0.1 mile per minute

The graph shows the relationship between distance driven and gallons of gas used. Use the graph to complete the statements. The car gets miles to the gallon. After the car has traveled miles, gallons of gas have been consumed.

30 80

Which graph represents viable values for y = 2x, where x is the number of pounds of rice scooped and purchased from a bulk bin at the grocery store and y is the total cost of the rice?

A

Rory is staying in a cabin on a hill 300 feet above sea level. She walks down the hill to the water's edge. The equation of her average change in elevation over time is e = 300 - 10t, where t is the time in minutes since she left the cabin, and e is her elevation with regard to sea level. Which values are viable points, and what are their values in the table relating t and e? a = b = c =

not viable 265 0

The vet told Jake that his dog, Rocco, who weighed 55 pounds, needed to lose 10 pounds. Jake started walking Rocco every day and changed the amount of food he was feeding him. Rocco lost half a pound the first week. Jake wants to determine Rocco's weight in pounds, p, after w weeks if Rocco continues to lose weight based on his vet's advice. The equation of the scenario is. The values of p must be.

p= 55 -0.5w any real number 45 to 55

Vlad spent 20 minutes on his history homework and then completely solved x math problems that each took 2 minutes to complete. What is the equation that can be used to find the value of y, the total time that Vlad spent on his homework, and what are the constraints on the values of x and y? y=2x+20; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20. y=2x+20; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 20. y=20x+2; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20. y=20x +2; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 20.

A. y=2x+20; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20.

Which graph represents viable values for y = 5.5x, where x is the number of cans of tomato paste and y is the total weight of the sealed cans in ounces?

B

Which would most likely be graphed using a continuous graph? Check all that apply. total cost, c, of buying b cans of beans total cost, c, of buying g pounds of broccoli speed of a car, s, as it accelerates over time, t number of stamps, s, needed to mail p postcards total distance, d, that has been driven over time, t decrease in outside temperature, F, one evening over time, t

B,C,E,F

The temperature, t, in degrees Fahrenheit, can be found by counting the number of cricket chirps, c, heard in 14 seconds and then adding 40. The equation t = c + 40 models the relationship between the temperature and the number of cricket chirps. What is true about the graph that represents this real-world scenario? Select two options. The graph is continuous. All values of t must be positive. A viable solution is (-2, 38). A viable solution is (0.5, 40.5). A viable solution is (10, 50).

B,E

Peaches are being sold for $2 per pound. The customer created a model to represent the total cost of peaches bought. If x represents the number of pounds of peaches bought and y represents the total cost of the peaches, which best describes the values of x and y? The values of both x and y can be any real number. The values of both x and y will be real numbers greater than or equal to 0. The value of x and y will always be zero The value of x can be any real number greater than or equal to 0, but the value of y must be an integer greater than or equal to 0.

B. The values of both x and y will be real numbers greater than or equal to 0.

The number of loaves of bread purchased and the total cost of the bread in dollars can be modeled by the equation c = 3.5b. Which table of values matches the equation and includes only viable solutions?

C

Read each relationship and decide whether its graph would be continuous or discrete?

Continuous graph : the height of a plant as it grows amount if fuel and distance traveled Discrete graph: amount of chairs for each table number of students per teacher

Each day that a library book is kept past its due date, a $0.30 fee is charged at midnight. Which ordered pair is a viable solution if x represents the number of days that a library book is late and y represents the total fee? (-3, -0.90) (-2.5, -0.75) (4.5, 1.35) (8, 2.40)

D. (8,2.40)

Jeff hiked for 2 hours and traveled 5 miles. If he continues at the same pace, which equation will show the relationship between the time, t, in hours he hikes to distance, d, in miles? Will the graph be continuous or discrete? d = 0.4t, discrete d = 0.4t, continuous d = 2.5t, discrete d = 2.5t, continuous

D. d = 2.5t, continuous

A 28,000-gallon swimming pool is being drained using a pump that empties 700 gallons per hour. Which equation models this situation if g is the number of gallons remaining in the pool and t is the amount of time in hours the pool has been draining? 28,000 = -700t 28,000g = -700t g = 700t - 28,000 g = 28,000 - 700t

D. g = 28,000 - 700t

Julie needs to cut 4 pieces of yarn, each with the same length, and a piece of yarn 7.75 inches long. Let x represent the length of each of the equal pieces of yarn that Julie decides to cut. What is the equation that can be used to determine the total length of all of the yarn that she ends up cutting, y? Is the graph of the equation continuous or discrete? y=7.75x+4; discrete y=7.75x+4; continuous y=4x+7.75; discrete y=4x+7.75; continuous

D. y=4x+7.75; continuous