Answers Algebra III AIntroduction to Linear Functions

Writing and Graphing Equations in Two Variables Answers

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Mr. Hann is trying to decide how many new copies of a book to order for his students. Each book weighs 6 ounces.

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The graph shows the relationship between the number of hours that Michelle has been driving and the distance that she has left to travel to get to her destination.

It took Michelle 6 hours to complete the trip.

For each hour that Michelle drove, she traveled an additional 50 miles.

In the first 6 hours, Michelle had traveled a total of 50 miles.

In the first 3 hours, Michelle had traveled a total of 200 miles.

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.

The graph shows the relationship between the number of minutes Maria spent jogging on a treadmill and the distance she jogged.

0.1 mile per minute

0.5 mile per minute

5 miles per minute

10 miles per minute

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, 1.20)

(8, 2.40)

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

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.

Which description is represented by a discrete graph?

Kiley bought a platter for $19 and several matching bowls that were $8 each. What is the total cost before tax?

The temperature at 9 a.m. was 83° F and is heating up at an average rate of 6°F per hour. What is the temperature x hours later?

Juan ate an egg with 78 calories and some cereal with 110 calories per serving for breakfast. What is the total amount of calories he consumed?

A bottle contained 2,000 mL of liquid and is being poured out at an average rate of 300 mL per second. How much liquid is left in the bottle after x seconds?

Which graph shows the equation V = 4 + 2t, where V is the total volume of water in a bucket and t is the elapsed time in minutes?

On a coordinate plane, the x-axis shows elapsed time in minutes (t) and the y-axis shows total volume of water (V). A straight line with a positive slope begins at point (0, 3) and ends at point (5.5, 24).

On a coordinate plane, the x-axis shows elapsed time in minutes (t) and the y-axis shows total volume of water (V). Solid circles are at points (0, 3), (1, 6), (2, 10), (3, 14), (4, 18), (5, 22).

On a coordinate plane, the x-axis shows elapsed time in minutes (t) and the y-axis shows total volume of water (V). A straight line with a positive slope begins at point (0, 4) and ends at point (6, 16).

On a coordinate plane, the x-axis shows elapsed time in minutes (t) and the y-axis shows total volume of water (V). Solid circles are at points (0, 4), (1, 6), (2, 8), (3, 10), (4, 12), (5, 14), (6, 16).

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

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.

The graph shows the relationship between the total cost and the number of gift cards that Raj bought for raffle prizes.

$80

$90

$100

$110

The graph below shows the amount of money left in the school’s desk fund, f, after d desks have been purchased.

$110

$135

$165

$190

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?

On a coordinate plane, x-axis is numbered negative 5 to positive 5 in increments of 1, and the y-axis is numbered negative 27.5 to 27.5 in increments of 5.5. A straight line with a positive slope begins at point (0, 0) and ends at point (5, 27.5)

On a coordinate plane, x-axis is numbered negative 5 to positive 5 in increments of 1, and the y-axis is numbered negative 27.5 to 27.5 in increments of 5.5. Solid circles appear at points (0, 0), (1, 5.5), (2, 11), (3, 16.5), (4, 22), (5, 27.5)

On a coordinate plane, x-axis is numbered negative 5 to 5 in increments of 1, and the y-axis is numbered negative 27.5 to 27.5 in increments of 5.5. A straight line with a positive slope begins at point (negative 5, negative 27.5) and ends at point (5, 27.5).

On a coordinate plane, x-axis is numbered negative 5 to 5 in increments of 1, and the y-axis is numbered negative 27.5 to 27.5 in increments of 5.5. Solid circles appear at points (negative 5, negative 27.5), (negative 4, negative 22), negative 3, negative 16.5), (negative 2, negative 11), (negative 1, negative 5.5), (0, 0), (1, 5.5), (2, 11), (3, 16.5), (4, 22), (5, 27.5)

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?

On a coordinate plane, a straight line with a positive slope begins at point (0, 0), and ends at point (2.5, 5).

On a coordinate plane, blue diamonds appear at points (0, 0), (1, 2), (2, 4).

On a coordinate plane, a straight line with a positive slope begins at point (negative 2.5, negative 5), crosses the x- and y-axis at point (0, 0), and ends at point (2.5, 5).

On a coordinate plane, blue diamonds appear at points (negative 2, negative 4), (negative 1, negative 2), (0, 0), (1, 2), (2, 4).

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Writing and Graphing Equations in Two Variables Answers

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