AnswersAlgebra IWriting and Graphing Equations in Two Variables

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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 is equal to 2 x plus 20 ; x is any integer greater than or equal to 0 , and y is an integer greater than or equal to 20 .
B
y is equal to 2 x plus 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 is equal to 20 x plus 2 ; x is any integer greater than or equal to 0 , and y is an integer greater than or equal to 20 .
D
y is equal to 20 x plus 2 ; x is any real number greater than or equal to 0 , and y is any real number greater than or equal to 20 .
2
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Otto used 5 point 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 ?

A
y is equal to x plus 5 point 5 ; x is any integer greater than or equal to 0 , and y is an integer greater than or equal to 5 .
B
y is equal to 5 point 5 x ; x is any real number greater than or equal to 0 , and y is any real number greater than or equal to 5 point 5 .
C
y is equal to x plus 5 point 5 ; x is any real number greater than or equal to 0 , and y is any real number greater than or equal to 5 point 5 .
D
y is equal to 5 point 5 x ; x is any integer greater than or equal to 0 , and y is an integer greater than or equal to 5 .
3

Peaches are being sold for 2 dollars 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 value of x and y will always be zero.
B
The values of both x and y can be any real number.
C
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 .
D
The values of both x and y will be real numbers greater than or equal to 0 .
4

Each day that a library book is kept past its due date, a 0 point 3 0 dollars 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
negative 2 point 5 comma negative 0 point 7 5
B
8 comma 2 point 4 0
C
negative 3 comma negative 0 point 9 0
D
4 point 5 comma 1 point 3 5
5

Mr. Hann is trying to decide how many new copies of a book to order for his students. Each book weighs 6 ounces. Which table contains only viable solutions if b represents the number of books he orders and w represents the total weight of the books, in ounces?

A
Table with 2 columns and 6 rows.Row 1: Column 1, 'Books b'; Column 2, 'Weight w' Row 2: Column 1, 'negative 1'; Column 2, 'negative 6' Row 3: Column 1, 'negative 0 point 5'; Column 2, 'negative 3' Row 4: Column 1, '0'; Column 2, '0' Row 5: Column 1, '0 point 5'; Column 2, '3' Row 6: Column 1, '1'; Column 2, '6'
B
Table with 2 columns and 6 rows.Row 1: Column 1, 'Books b'; Column 2, 'Weight w' Row 2: Column 1, '0'; Column 2, '0' Row 3: Column 1, '0 point 5'; Column 2, '3' Row 4: Column 1, '1'; Column 2, '6' Row 5: Column 1, '1 point 5'; Column 2, '9' Row 6: Column 1, '2'; Column 2, '12'
C
Table with 2 columns and 6 rows.Row 1: Column 1, 'Books b'; Column 2, 'Weight w' Row 2: Column 1, 'negative 2'; Column 2, 'negative 12' Row 3: Column 1, 'negative 1'; Column 2, 'negative 6' Row 4: Column 1, '0'; Column 2, '0' Row 5: Column 1, '1'; Column 2, '6' Row 6: Column 1, '2'; Column 2, '12'
D
Table with 2 columns and 6 rows.Row 1: Column 1, 'Books b'; Column 2, 'Weight w' Row 2: Column 1, '0'; Column 2, '0' Row 3: Column 1, '1'; Column 2, '6' Row 4: Column 1, '2'; Column 2, '12' Row 5: Column 1, '3'; Column 2, '18' Row 6: Column 1, '4'; Column 2, '24'
6

Which graph shows the equation cap v is equal to 4 plus 2 t , where cap v is the total volume of water in a bucket and t is the elapsed time in minutes?

A
Image with description 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 comma 3), (1 comma 6), (2 comma 10), (3 comma 14), (4 comma 18), (5 comma 22).
B
Image with description 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 comma 4), (1 comma 6), (2 comma 8), (3 comma 10), (4 comma 12), (5 comma 14), (6 comma 16).
C
Image with description 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 comma 4) and ends at point (6 comma 16).
D
Image with description 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 comma 3) and ends at point (5 point 5 comma 24).
7

Which graph represents viable values for y is equal to 2 x , 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
Image with description On a coordinate plane, a straight line with a positive slope begins at point (negative 2 point 5 comma negative 5), crosses the x- and y-axis at point (0 comma 0), and ends at point (2 point 5 comma 5).
B
Image with description On a coordinate plane, blue diamonds appear at points (negative 2 comma negative 4), (negative 1 comma negative 2), (0 comma 0), (1 comma 2), (2 comma 4).
C
Image with description On a coordinate plane, blue diamonds appear at points (0 comma 0), (1 comma 2), (2 comma 4).
D
Image with description On a coordinate plane, a straight line with a positive slope begins at point (0 comma 0), and ends at point (2.5 comma 5).
8

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 ?

A
y is equal to 4 plus x
B
y is equal to x minus 4
C
y is equal to x divided by 4
D
y is equal to 4 times x
9

Which graph represents viable values for y is equal to 5 point 5 x , where x is the number of cans of tomato paste and y is the total weight of the sealed cans in ounces?

A
Image with description 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 comma negative 27 point 5) and ends at point (5 comma 27 point 5).
B
Image with description 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 comma negative 27.5), (negative 4 comma negative 22), negative 3 comma negative 16.5), (negative 2 comma negative 11), (negative 1 comma negative 5.5), (0 comma 0), (1 comma 5.5), (2 comma 11), (3 comma 16.5), (4 comma 22), (5 comma 27.5)
C
Image with description 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 point 5 to 27 point 5 in increments of 5 point 5. A straight line with a positive slope begins at point (0 comma 0) and ends at point (5 comma 27 point 5)
D
Image with description 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 comma 0), (1 comma 5.5), (2 comma 11), (3 comma 16.5), (4 comma 22), (5 comma 27.5)
10

Julie needs to cut 4 pieces of yarn, each with the same length, and a piece of yarn 7 point 7 5 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 is equal to 7 point 7 5 x plus 4 ; continuous
B
y is equal to 7 point 7 5 x plus 4 ; discrete
C
y is equal to 4 x plus 7 point 7 5 ; continuous
D
y is equal to 4 x plus 7 point 7 5 ; discrete

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