AnswersRVACR Reading Common Core Algebra IQuantitative Reasoning

Writing and Graphing Equations in Two Variables Answers

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

Question illustration
A
$110
B
$135
C
$165
D
$190
2
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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
On a coordinate plane, a straight line with a positive slope begins at point (0, 0), and ends at point (2.5, 5).
Option A
B
On a coordinate plane, blue diamonds appear at points (0, 0), (1, 2), (2, 4).
Option B
C
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).
Option C
D
On a coordinate plane, blue diamonds appear at points (negative 2, negative 4), (negative 1, negative 2), (0, 0), (1, 2), (2, 4).
Option D
3

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.
Option
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.
Option
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.
Option
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.
Option
4

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?

A
(–3, –0.90)
B
(–2.5, –0.75)
C
(4.5, 1.20)
D
(8, 2.40)
5

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?

A
The values of both x and y can be any real number.
B
The values of both x and y will be real numbers greater than or equal to 0.
C
The value of x and y will always be zero
D
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.
6

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?

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.
B
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.
C
y=20x+2; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20.
D
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.
7

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?

A
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).
Option A
B
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).
Option B
C
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).
Option C
D
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).
Option D
8

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?

A
y=7.75x+4; discrete
B
y=7.75x+4; continuous
C
y=4x+7.75; discrete
D
y=4x+7.75; continuous
9

On a coordinate plane, a straight line with a positive slope begins at point (0, 50) and ends at point (5.5, 600).

Question illustration
A
the total amount of money in the cash register, y, containing $50 in change and small bills and x $100 bills
B
the total number of puzzle pieces, y, in a brand new 50-piece puzzle, and x brand-new 100-piece puzzles
C
the total weight of the barbell, y, where the bar weighs 50 pounds and x 100-pound weights are added to it
D
the total number of calories, y, in a salad with vegetables containing 50 calories topped with x ounces of salad dressing at 100 calories per ounce
10

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

Question illustration
A
$80
B
$90
C
$100
D
$110

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