Deck 3: Linear Equations in Two Variables

Question 1

Plot the given point in a rectangular coordinate system.

- $( - 5 , - 6 )$

A)
B)
C)
D)

Answer 1

Question 2

Plot the given point in a rectangular coordinate system.
$(0,5)$

A)
B)
C)
D)

Answer 2

Question 3

Indicate in which quadrant the point lies.
$\left( \frac { 3 } { 8 } , - \frac { 2 } { 5 } \right)$

A) II
B) I
C) IV
D) III

Answer 3

IV

Question 4

Indicate in which quadrant the point lies.
$$\left( - \frac { 3 } { 8 } , - \frac { 1 } { 2 } \right)$$

A) III
B) IV
C) I
D) II

Question 5

Give the ordered pairs that correspond to the points labeled in the figure.

A) R = (-5, -5), S = (3, -5)
B) R = (-5, 3), S = (-3, -5)
C) R = (3, 6), S = (-5, -3)
D) R = (-5, 3), S = (-5, -3)

Question 6

Indicate in which quadrant the point lies.
(-2, 17)

A) II
B) III
C) IV
D) I

Question 7

Indicate in which quadrant the point lies.
(9, -15)

A) I
B) III
C) IV
D) II

Question 8

Plot the given point in a rectangular coordinate system.

- $\left( 0 , - \frac { 11 } { 2 } \right)$

A)
B)
C)
D)

Question 9

Plot the given point in a rectangular coordinate system.

- $\left( \frac { 3 } { 2 } , - \frac { 9 } { 2 } \right)$

A)
B)
C)
D)

Question 10

Plot the given point in a rectangular coordinate system.

- $(-4,0)$

A)
B)
C)
D)

Question 11

Indicate in which quadrant the point lies.
(-11, -10)

A) II
B) III
C) I
D) IV

Question 12

Give the ordered pairs that correspond to the points labeled in the figure.

A) A = (7, 20), B = (3, -4)
B) A = (2, 7), B = (3, -4)
C) A = (2, 7), B = (-4, 3)
D) A = (2, 3), B = (7, 3)

Question 13

Plot the given point in a rectangular coordinate system.

- $\left( - \frac { 3 } { 2 } , 0 \right)$

A)
B)
C)
D)

Question 14

Plot the given point in a rectangular coordinate system.
$(-3,-5)$

A)
B)
C)
D)

Question 15

Plot the given point in a rectangular coordinate system.
$(6,-3)$

A)
B)
C)
D)

Question 16

Indicate in which quadrant the point lies.
$$\left( - \frac { 1 } { 3 } , \frac { 2 } { 3 } \right)$$

A) II
B) III
C) I
D) IV

Question 17

Plot the given point in a rectangular coordinate system.
$(5,4)$

A)
B)
C)
D)

Question 18

Indicate in which quadrant the point lies.
(9, 12)

A) IV
B) II
C) III
D) I

Question 19

Plot the given point in a rectangular coordinate system.
$(-4,3)$

A)
B)
C)
D)

Question 20

Give the ordered pairs that correspond to the points labeled in the figure.

A) C = (-4, -5), D = (5, -5)
B) C = (-4, 5), D = (5, -5)
C) C = (5, 8), D = (-5, 5)
D) C = (-4, 5), D = (-5, 5)

Question 21

Determine whether the ordered pair is a solution of the given equation.
(-1, -3) x - y = 4

A) No
B) Yes

Question 22

Determine whether the ordered pair is a solution of the given equation.
(3, 6) y = x - 9

A) Yes
B) No

Question 23

Determine whether the ordered pair is a solution of the given equation.
(-3, 6) 3x + 4y = 15

A) Yes
B) No

Question 24

Graph the linear equation in two variables.
$y=-x+3$

A)
B)
C)
D)

Question 25

Find a solution to the equation using the value given for x.
y = 4x + 7; x = -2

A) (-2, -18)
B) (-2, -1)
C) (-2, 11)
D) (-2, -22)

Question 26

Determine whether the ordered pair is a solution of the given equation.
(4, -5) y = x - 9

A) Yes
B) No

Question 27

Determine whether the ordered pair is a solution of the given equation.
(1, 1) 3x + 4y = -1

A) No
B) Yes

Question 28

Determine whether the ordered pair is a solution of the given equation.
(6, 1) x - y = 5

A) No
B) Yes

Question 29

Graph the linear equation in two variables.
y = 4x

A)
B)
C)
D)

Question 30

Graph the linear equation in two variables.
$$y = \frac { 1 } { 6 } x + 6$$

A)
B)
C)
D)

Question 31

Graph the linear equation in two variables.
$y=-3 x-3$

A)
B)
C)
D)

Question 32

Find a solution to the equation using the value given for x.
y = -5x - 2; x = 6

A) (6, -28)
B) (6, -32)
C) (6, -7)
D) (6, -42)

Question 33

Find a solution to the equation using the value given for x.
y = -7x - 5; x = 0

A) (0, -12)
B) (0, 7)
C) (0, -5)
D) (0, 0)

Question 34

Graph the linear equation in two variables.
$y=x-2$

A)
B)
C)
D)

Question 35

Find a solution to the equation using the value given for x.
y = 4x; x = 3.

A) (3, -1)
B) (3, 15)
C) (3, 12)
D) (3, 7)

Question 36

Graph the linear equation in two variables.
$y=-6 x$

A)
B)
C)
D)

Question 37

Give the ordered pairs that correspond to the points labeled in the figure.

A) G = (2, 4), H = (-7, 2)
B) G = (4, 20), H = (2, -7)
C) G = (2, 4), H = (2, -7)
D) G = (2, 2), H = (4, 2)

Question 38

Find a solution to the equation using the value given for x.
y = -4x; x = 6.

A) (6, 10)
B) (6, -24)
C) (6, -18)
D) (6, 2)

Question 39

Find a solution to the equation using the value given for x.
y = 8x - 5; x = 5

A) (5, 35)
B) (5, 45)
C) (5, 3)
D) (5, 15)

Question 40

Graph the linear equation in two variables.
$y=4 x-2$

A)
B)
C)
D)

Question 41

Solve the problem.
The linear equation in two variables y = 124 - 2x models the amount of water, y, in ounces, remaining in a leaky bucket x minutes after the bucket was filled. The equation indicates that the bucket initially contains 124 ounces
Of water and loses 2 ounces each minute. Find a solution of y = 124 - 2x using 4 for x.

A) (4, 8)
B) (4, 132)
C) (4, 116)
D) (4, 122)

Question 42

Solve the problem.
A customer at a store bought 8 bottles of juice and 4 fruit pies for a total cost of $60.00. If a bottle of juice costs $3.25, find the cost of a fruit pie.

A) $7.50
B) $9.25
C) $8.50
D) $8.00

Question 43

Graph using a graphing utility and identify the x- and y-intercepts from the graph. Use the indicated graphing window
dimensions.
2x + 5y = 30 (window size [0, 15, 1] by [-10, 10, 1])

A) No $x$ -intercept; $y$ -intercept $= 6$
\
B)(x \text {-intercept }=15 ; y \text {-intercept }=-6\)


C) $x$ -intercept $= 15 ; y$ -intercept $= 6$


D) $x$ -intercept $= 4 ; y$ -intercept $= 15$

Question 44

Use the graph to identify the x- and y- intercepts or state that there is no x- or y-intercept.

A) x-intercept = -5; no y-intercept
B) no x-intercept; y-intercept = -5
C) x-intercept = -5; y-intercept = 0
D) x-intercept = 0; y-intercept = 5

Question 45

Use the graph to identify the x- and y- intercepts or state that there is no x- or y-intercept.

A) x-intercept = -5; y-intercept = 0
B) no x-intercept; y-intercept = -5
C) x-intercept = -5; y-intercept = 5
D) x-intercept = -5; no y-intercept

Question 46

The graph shows the monthly revenue in millions of dollars of a growing company after the company doubled its advertising. Use the graph to solve the problem.
During what period of time is the company's monthly revenue decreasing?

A) From the time that the advertising was doubled until the 9th month
B) From the time that the advertising was doubled until the 6th month
C) From the 9th month to the 12th month
D) From the 6th month to the 9th month

Question 47

The graph shows the monthly revenue in millions of dollars of a growing company after the company doubled its advertising. Use the graph to solve the problem.
Estimate the maximum revenue during the period of time plotted on the graph.

A) $7 million
B) $10 million
C) $9 million
D) $5 million

Question 48

Use the graph to identify the x- and y- intercepts or state that there is no x- or y-intercept.

A) x-intercept = 2; y-intercept = 8
B) x-intercept = 2; y-intercept = -8
C) x-intercept = -8; y-intercept = 8
D) x-intercept = -2; y-intercept = 8

Question 49

Solve the problem.
A projectile is fired from the top of a building 200 feet high. The graph shows the height of the projectile, in feet, above the ground, in terms of its distance, in feet, from the base of the building. Estimate the coordinates of the point A. Interpret the coordinates in terms of the information given.

A) approximately (1350, 200); the projectile is 1350 feet above the ground 200 seconds after it is fired.
B) approximately (1350, 200); the projectile is 1350 feet above the ground when it is 200 feet from the base of the building.
C) approximately (1350, 200); the projectile is 200 feet above the ground when it is 1350 feet from the base of the building.
D) approximately (200, 1350); the projectile is 1350 feet from the base of the building 200 seconds after it is fired

Question 50

Write the sentence as a linear equation in two variables. Then graph the equation.
The y-variable is 2 less than 7 times the x-variable.

A) $y = 7 x - 2$

B) $y = 2 - 7 x$

C) $y = 2 x - 7$

D) $y = 7 ( x - 2 )$
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Question 51

Use the graph to identify the x- and y- intercepts or state that there is no x- or y-intercept.

A) x-intercept = -1; y-intercept = 6
B) x-intercept = 1; y-intercept = 6
C) x-intercept = -6; y-intercept = -6
D) x-intercept = -1; y-intercept = -6

Question 52

Solve the problem.
The linear equation in two variables y = 3x + 80 models the total cost, y, in dollars, for towing a car x miles. The equation indicates that the towing company charges a fixed amount of $80 to send a truck to pick up the car
Plus a cost of $3 for each mile the car is towed. Find a solution of y = 3x + 80 using 13 for x.

A) (13, 83)
B) (13, 39)
C) (13, 119)
D) (13, 109)

Question 53

Solve the problem.
A customer at a store bought 4 bottles of juice and 7 fruit pies for a total cost of $81.50. If x represents the cost of a bottle of juice and y represents the cost of one fruit pie, write an equation in two variables that reflects the
Given conditions.

A) (4 + x) + (7 + y) = 81.50
B) (4 + x)(7 + y) = 81.50
C) 4x + 7y = 81.50
D) 7x + 4y = 81.50

Question 54

Use the graph to identify the x- and y- intercepts or state that there is no x- or y-intercept.

A) x-intercept = -1; y-intercept = -5
B) x-intercept = 1; y-intercept = -5
C) x-intercept = 1; y-intercept = 5
D) x-intercept = -5; y-intercept = 5

Question 55

Write the sentence as a linear equation in two variables. Then graph the equation.
The y-variable is 7 less than the x-variable.

A) $y = \frac { x } { 7 }$

B) $y = x - 7$

C) $y = 7 - x$

D) $y - 7 = x$

Question 56

The graph shows the monthly revenue in millions of dollars of a growing company after the company doubled its advertising. Use the graph to solve the problem.
During what period of time is the company's monthly revenue increasing?

A) From the 9th month to the 12th month
B) From the 6th month to the 9th month
C) From the time that the advertising was doubled until the 9th month
D) From the time that the advertising was doubled until the 6th month

Question 57

Solve the problem.
The linear equation in two variables y = 0.10x + 200 models the total weekly cost, y, in dollars, for renting a car and driving it x miles. The equation indicates that the rental company charges a fixed amount of $200 for the
Week plus a cost of $0.10 for each mile the car is driven. Find a solution of y = 0.10x + 200 using 220 for x.

A) (220, 2200)
B) (220, 222)
C) (220, 197)
D) (220, 182)

Question 58

Solve the problem.
A projectile is fired from the top of a building 200 feet high. The graph shows the height of the projectile, in feet, above the ground, in terms of its distance, in feet, from the base of the building. What is the maximum height of the projectile? What is the distance of the projectile from the base of the building when it
Reaches its maximum height?

A) 1635 feet; 676 feet
B) 396 feet; 676 feet
C) 676 feet; 396 feet
D) 396 feet; 1635 feet

Question 59

Graph using a graphing utility and identify the x- and y-intercepts from the graph. Use the indicated graphing window
dimensions.
$x - 3 y = 6$ (window size $[ - 10,10,1 ]$ by $[ - 10,10,1 ]$ )

A) $x$ -intercept $= - 3 ; y$ -intercept $= - \frac { 1 } { 2 }$

B) $x \text {-intercept }=-6 ; y \text {-intercept }=-2$

C) $x \text {-intercept }=-2 ; y \text {-intercept }=6$

D) $x \text {-intercept }=6 ; y \text {-intercept }=-2$

Question 60

Solve the problem.
The linear equation in two variables y = 1100x + 2660 models the altitude above sea level, y, in feet, of an airplane x minutes after taking off from a high plateau. The equation indicates that the airplane's altitude is
Initially 2660 feet above sea level and increases 1100 feet each minute. Find a solution of y = 1100x + 2660 using
4 for x.

A) (4, 7060)
B) (4, 7160)
C) (4, 4400)
D) (4, 6960)

Question 61

Find the y- and x-intercepts for the equation. Then graph the equation.
x + y = 3

A) $( 0,3 ) , ( - 3,0 )$
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B) $( 0,3 ) , ( 3,0 )$

C) $( 0 , - 3 ) , ( 3,0 )$

D) $( 0 , - 3 ) , ( - 3,0 )$

Question 62

The graph shows the monthly revenue in millions of dollars of a growing company after the company doubled its advertising. Use the graph to solve the problem.
4x - 20y = 20

A) x-intercept = -1; y-intercept = 5
B) x-intercept = 5; y-intercept = 1
C) x-intercept = 1; y-intercept = 5
D) x-intercept = 5; y-intercept = -1

Question 63

The graph shows the monthly revenue in millions of dollars of a growing company after the company doubled its advertising. Use the graph to solve the problem.
2x - 4y = 5

A) $x$ -intercept $= 3 ; y$ -intercept $= 9$
B) $x$ -intercept $= \frac { 5 } { 2 } ; y$ -intercept $= \frac { 5 } { 4 }$
C) $x$ -intercept $= \frac { 5 } { 2 } ; y$ -intercept $= - \frac { 5 } { 4 }$
D) $x$ -intercept $= - \frac { 5 } { 4 } ; y$ -intercept $= \frac { 5 } { 2 }$

Question 64

Find the y- and x-intercepts for the equation. Then graph the equation.
4x - y = 2

A) $( 0 , - 2 ) ; \left( - \frac { 1 } { 2 } , 0 \right)$

B) $( 0 , - 2 ) ; \left( \frac { 1 } { 2 } , 0 \right)$

C) $\left( 0 , - \frac { 1 } { 2 } \right) ; ( - 2,0 )$

D) $\left( 0 , \frac { 1 } { 2 } \right) ; ( - 2,0 )$

Question 65

Find the y- and x-intercepts for the equation. Then graph the equation.
-4x - 12y = 12

A) $( 0 , - 1 ) ; ( 3,0 )$

B) $( 0,1 ) ; ( 3,0 )$

C) $( 0,1 ) ; ( - 3,0 )$

D) $( 0 , - 1 ) ; ( - 3,0 )$

Question 66

Write an equation for the graph.

A) y = -3
B) x = -3
C) y = 3
D) x = 3

Question 67

Find the y- and x-intercepts for the equation. Then graph the equation.
x - 2y = 6

A) $( 0 , - 3 ) ; ( - 6,0 )$

B) $( 0 , - 3 ) ; ( 6,0 )$

C) $( 0,3 ) ; ( - 6,0 )$

D) $( 0,3 ) ; ( 6,0 )$

Question 68

Graph the equation.
y = 8

A)
B)
C)
D)

Question 69

Find the y- and x-intercepts for the equation. Then graph the equation.
25y - 5x = -10

A) $\left( 0 , \frac { 2 } { 5 } \right) ; ( - 2,0 )$

B) $\left( 0 , \frac { 2 } { 5 } \right) ; ( 2,0 )$

C) $\left( 0 , - \frac { 2 } { 5 } \right) ; ( 2,0 )$

D) $\left( 0 , - \frac { 2 } { 5 } \right) ; ( - 2,0 )$

Question 70

Find the y- and x-intercepts for the equation. Then graph the equation.
4x - 8y = 0

A) $( 0,0 )$ ; $( 0,0 )$

B) $( 0,0 ) ; ( 0,0 )$

C) $( 0,0 ) ; ( 0,0 )$

D) $( 0,0 ) ; ( 0,0 )$

Question 71

Graph the equation.
y + 3 = 0

A)
B)
C)
D)

Question 72

The graph shows the monthly revenue in millions of dollars of a growing company after the company doubled its advertising. Use the graph to solve the problem.
How many months after the company doubled its advertising did the minimum monthly revenue occur.

A) 9 months
B) 6 months
C) 0 months
D) 12 months

Question 73

The graph shows the monthly revenue in millions of dollars of a growing company after the company doubled its advertising. Use the graph to solve the problem.
What is the y-intercept?

A) 1
B) 4
C) 2
D) 6

Question 74

Write an equation for the graph.

A) x = -6
B) y = 6
C) y = -6
D) x = 6

Question 75

The graph shows the monthly revenue in millions of dollars of a growing company after the company doubled its advertising. Use the graph to solve the problem.
10x - 2y = -6

A) $x$ -intercept $= \frac { 3 } { 5 } ; y$ -intercept $= 3$
B) $x$ -intercept $= - \frac { 3 } { 5 } ; y$ -intercept $= - 3$
C) $x$ -intercept $= - \frac { 3 } { 5 } ; y$ -intercept $= 3$
D) $x$ -intercept $= 3 ; y$ -intercept $= - \frac { 3 } { 5 }$

Question 76

Find the y- and x-intercepts for the equation. Then graph the equation.
2x - 4y = 4

A) $( 0,1 ) ; ( 2,0 )$

B) $( 0 , - 1 ) ; ( - 2,0 )$

C) $( 0 , - 1 ) ; ( 2,0 )$

D) $( 0,1 ) ; ( - 2,0 )$

Question 77

Graph the equation.
x = 6

A)
B)
C)
D)

Question 78

The graph shows the monthly revenue in millions of dollars of a growing company after the company doubled its advertising. Use the graph to solve the problem.
How many months after the company doubled its advertising did the maximum monthly revenue occur.

A) 9 months
B) 0 months
C) 6 months
D) 12 months

Question 79

The graph shows the monthly revenue in millions of dollars of a growing company after the company doubled its advertising. Use the graph to solve the problem.
Estimate the minimum revenue during the period of time plotted on the graph.

A) $2 million
B) $4 million
C) $1 million
D) $6 million

Question 80

Find the y- and x-intercepts for the equation. Then graph the equation.
2y - x = 0

A) $( 0,0 ) , ( 0,0 )$

B) $( 0 , - 2 ) , ( 2,0 )$

C) $( 0,2 ) , ( - 2,0 )$

D) $( 0,0 ) , ( 0,0 )$