Deck 3: Graphs of Linear Equations

Question 1

Find the coordinates of the labeled points.

A) $\mathrm { A } ( - 6,0 ) ; \mathrm { B } ( 4 , - 4 )$
B) $\mathrm { A } ( 6,0 ) ; \mathrm { B } ( 4 , - 4 )$
C) $\mathrm { A } ( - 6,6 ) ; \mathrm { B } ( 4 , - 4 )$
D) $A ( - 6,0 ) ; B ( - 4 , - 4 )$

Answer 1

A

Question 2

Determine whether the given ordered pair is a solution of the equation.

- $$x + y = 12 ; ( 7,5 )$$

Answer 2

True

Question 3

Write the word or phrase that best completes each statement or answers the question.
Plot the ordered pairs on the rectangular coordinate system provided.
List the quadrant(s)in which the given point is located.
(4, 9)

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

Answer 3

B

Question 4

Determine whether the given ordered pair is a solution of the equation.

- $$x - y = 25 ; ( 5,4 )$$

Question 5

Find the coordinates of the labeled points.

A) $\mathrm { A } ( 5 , - 2 ) ; \mathrm { B } ( 1 , - 4 )$
B) $\mathrm { A } ( 5,2 ) ; \mathrm { B } ( 0 , - 4 )$
C) $\mathrm { A } ( 5,2 ) ; \mathrm { B } ( 0,4 )$
D) $\mathrm { A } ( - 5,2 ) ; \mathrm { B } ( 0,4 )$

Question 6

Find the coordinates of the labeled points.

A) $\mathrm { A } ( 2,6 ) ; \mathrm { B } ( 7 , - 6 )$
B) $\mathrm { A } ( 2,7 ) ; \mathrm { B } ( 6,7 )$
C) $\mathrm { A } ( 6,20 ) ; \mathrm { B } ( 7 , - 6 )$
D) $\mathrm { A } ( 2,6 ) ; \mathrm { B } ( - 6,7 )$

Question 7

Write the word or phrase that best completes each statement or answers the question.
Plot the ordered pairs on the rectangular coordinate system provided.
List the quadrant(s)in which the given point is located.
$( - 6,0 )$

A) IV
B) III
C) II
D) On an axis

Question 8

Determine whether the given ordered pair is a solution of the equation.

- $$x + y = 14 ; ( 7,4 )$$

Question 9

Write the word or phrase that best completes each statement or answers the question.
Plot the ordered pairs on the rectangular coordinate system provided.
List the quadrant(s)in which the given point is located.
$$( - 10 , - 20 )$$

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

Question 10

Find the coordinates of the labeled points.

A) $\mathrm { G } ( 7,2 ) ; \mathrm { H } ( - 5 , - 7 )$
B) $\mathrm { G } ( 2,30 ) ; \mathrm { H } ( - 5 , - 7 )$
C) $\mathrm { G } ( 7 , - 5 ) ; \mathrm { H } ( 2 , - 5 )$
D) $\mathrm { G } ( 7,2 ) ; \mathrm { H } ( - 7 , - 5 )$

Question 11

Write the word or phrase that best completes each statement or answers the question.
Plot the ordered pairs on the rectangular coordinate system provided.
List the quadrant(s)in which the given point is located.
The first coordinate is positive.

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

Question 12

Write the word or phrase that best completes each statement or answers the question.
Plot the ordered pairs on the rectangular coordinate system provided.
List the quadrant(s)in which the given point is located.
The second coordinate is negative.

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

Question 13

Write the word or phrase that best completes each statement or answers the question.
Plot the ordered pairs on the rectangular coordinate system provided.
List the quadrant(s)in which the given point is located.
$( 14 , - 12 )$

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

Question 14

Find the coordinates of the labeled points.

A) $\mathrm { C } ( 6,10 ) ; \mathrm { D } ( - 4,3 )$
B) $C ( - 3 , - 4 ) ; \mathrm { D } ( 6 , - 4 )$
C) $\mathrm { C } ( - 3,6 ) ; \mathrm { D } ( 3 , - 4 )$
D) $\mathrm { C } ( - 3,6 ) ; \mathrm { D } ( - 4,3 )$

Question 15

Determine whether the given ordered pair is a solution of the equation.

-3x + y = 18; (5, 3)

Question 16

Write the word or phrase that best completes each statement or answers the question.
Plot the ordered pairs on the rectangular coordinate system provided.
List the quadrant(s)in which the given point is located.
$( - 4,6 )$

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

Question 17

Write the word or phrase that best completes each statement or answers the question.
Plot the ordered pairs on the rectangular coordinate system provided.
List the quadrant(s)in which the given point is located.
$$( - 2.7 , - 3.7 )$$

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

Question 18

Write the word or phrase that best completes each statement or answers the question.
Plot the ordered pairs on the rectangular coordinate system provided.
List the quadrant(s)in which the given point is located.
$$\left( \frac { 2 } { 3 } , - \frac { 6 } { 13 } \right)$$

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

Question 19

Find the coordinates of the labeled points.

A) $\mathrm { E } ( 2,10 ) ; \mathrm { G } ( - 5 , - 6 )$
B) $\mathrm { E } ( - 3 , - 5 ) ; \mathrm { G } ( 2 , - 5 )$
C) $\mathrm { E } ( - 3,2 ) ; \mathrm { G } ( - 6 , - 5 )$
D) $\mathrm { E } ( - 3,2 ) ; \mathrm { G } ( - 5 , - 6 )$

Question 20

Write the word or phrase that best completes each statement or answers the question.
Plot the ordered pairs on the rectangular coordinate system provided.
List the quadrant(s)in which the given point is located.
The coordinates have the same sign.

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

Question 21

Write the word or phrase that best completes each statement or answers the question.
Show that the two ordered pairs are solutions to the given equation. Then use the graph of the two points to determine
another solution. Answers may vary.
Graph the linear equation.
$y=\frac{1}{5} x+\frac{7}{5}$

A)

B)

C)

D)

Question 22

Find the coordinates of the y-intercept for the given equation.
$4 x - 2 y = 8$

A) $( 0,4 )$
B) $( 0 , - 4 )$
C) $( 4,2 )$
D) $( 0,8 )$

Question 23

Write the word or phrase that best completes each statement or answers the question.
Show that the two ordered pairs are solutions to the given equation. Then use the graph of the two points to determine
another solution. Answers may vary.
Graph the linear equation.
$-4 x+y=0$

A)

B)

C)

D)

Question 24

Write the word or phrase that best completes each statement or answers the question.
Show that the two ordered pairs are solutions to the given equation. Then use the graph of the two points to determine
another solution. Answers may vary.
Graph the linear equation.
$-x+8 y=-3$

A)

B)

C)

D)

Question 25

Write the word or phrase that best completes each statement or answers the question.
Show that the two ordered pairs are solutions to the given equation. Then use the graph of the two points to determine
another solution. Answers may vary.
Graph the linear equation.
$-9 x-y=0$

A)

B)

C)

D)

Question 26

Find the coordinates of the y-intercept for the given equation.
$$y = \frac { 1 } { 6 } x + 4$$

A) $\left( 0 , \frac { 1 } { 6 } \right)$
B) $( 4,0 )$
C) $\left( \frac { 1 } { 6 } , 4 \right)$
D) $( 0,4 )$

Question 27

Write the word or phrase that best completes each statement or answers the question.
Show that the two ordered pairs are solutions to the given equation. Then use the graph of the two points to determine
another solution. Answers may vary.
Graph the linear equation.
$x+8 y=5$

A)

B)

C)

D)

Question 28

Write the word or phrase that best completes each statement or answers the question.
Show that the two ordered pairs are solutions to the given equation. Then use the graph of the two points to determine
another solution. Answers may vary.
Graph the linear equation.
$$y = \frac { 5 } { 3 } x - 2$$

A)

B)

C)

D)

Question 29

Find the coordinates of the y-intercept for the given equation.
$$y = x - 3$$

A) $( 0,3 )$
B) $( 0 , - 3 )$
C) $( - 3,0 )$
D) $( 0,1 )$

Question 30

Find the coordinates of the y-intercept for the given equation.
$$x + 2 y = 3$$

A) $( 6,0 )$
B) $( 0,6 )$
C) $( 2,6 )$
D) $\left( 0 , \frac { 3 } { 2 } \right)$

Question 31

Write the word or phrase that best completes each statement or answers the question.
Show that the two ordered pairs are solutions to the given equation. Then use the graph of the two points to determine
another solution. Answers may vary.
Graph the linear equation.
$y=3 x$

A)

B)

C)

D)

Question 32

Determine whether the given ordered pair is a solution of the equation.

- $$5 x - 4 y = 32 ; ( 4,3 )$$

Question 33

Write the word or phrase that best completes each statement or answers the question.
Show that the two ordered pairs are solutions to the given equation. Then use the graph of the two points to determine
another solution. Answers may vary.
Graph the linear equation.
$y=2 x+3$

A)

B)

C)

D)

Question 34

Determine whether the given ordered pair is a solution of the equation.

- $$2 x + 5 y = 29 ; ( 2,5 )$$

Question 35

Write the word or phrase that best completes each statement or answers the question.
Show that the two ordered pairs are solutions to the given equation. Then use the graph of the two points to determine
another solution. Answers may vary.
Graph the linear equation.
$4 x-y=8$

A)

B)

C)

D)

Question 36

Find the coordinates of the y-intercept for the given equation.
$x + y = - 7$

A) $( 0 , - 7 )$
B) $( 0,7 )$
C) $( 7,0 )$
D) $( 0 , - 1 )$

Question 37

Find the coordinates of the y-intercept for the given equation.
$$y = \frac { 9 } { 2 } x$$

A) $\left( 1 , \frac { 9 } { 2 } \right)$
B) $\left( 0 , \frac { 9 } { 2 } \right)$
C) $( 0,0 )$
D) $\left( \frac { 9 } { 2 } , 0 \right)$

Question 38

Find the coordinates of the y-intercept for the given equation.
$$y = 8 x - 9$$

A) $( 0,9 )$
В) $( 0 , - 9 )$
C) $( 8 , - 9 )$
D) $( - 9,0 )$

Question 39

Find the coordinates of the y-intercept for the given equation.
$$y = x + 7$$

A) $( 7,7 )$
B) $( 0,7 )$
C) $( 7,0 )$
D) $( 0,1 )$

Question 40

Write the word or phrase that best completes each statement or answers the question.
Show that the two ordered pairs are solutions to the given equation. Then use the graph of the two points to determine
another solution. Answers may vary.
Graph the linear equation.
$2 y+6 x=14$

A)

B)

C)

D)

Question 41

Find the coordinates of the y-intercept and the coordinates of the x-intercept.

A) $( 0 , - 5 ) , ( - 1,0 )$
B) $( 0 , - 1 ) , ( - 5,0 )$
C) $( - 1 , - 5 ) , ( 0,0 )$
D) $( 0,0 ) , ( - 5 , - 1 )$

Question 42

Find the x- and y-intercepts for the equation. Then graph the equation.
$$2 x - 5 = y$$

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

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

Question 43

Find the coordinates of the y-intercept and the x-intercept, in that order.
$$3 x + y = 3$$

A) $( 1,0 ) ( 0,3 )$
B) $( 0 , - 1 ) ( 0,6 )$
C) $( 3,6 ) ( - 1,3 )$
D) $( - 1,0 ) ( 6,0 )$

Question 44

Find the x- and y-intercepts for the equation. Then graph the equation.
$-6 x-30 y=30$

A) $( 0 , - 1 ) , ( 5,0 )$

В) $( 0 , - 1 ) , ( - 5,0 )$

Question 45

Find the coordinates of the y-intercept and the x-intercept, in that order.
$$- 2 x + 5 y = 0$$

A) $( 0 , - 2 ) ( - 1,0 )$
В) $( 0,0 ) ( 0,0 )$
C) $( 0 , - 1 ) ( 0 , - 2 )$
D) $( - 1,0 ) ( - 2,0 )$

Question 46

Find the coordinates of the y-intercept for the given equation.
$$8 y + 8 x = - 4$$

A) $\left( - \frac { 1 } { 2 } , 0 \right)$
B) $\left( 0 , - \frac { 1 } { 2 } \right)$
C) $( 0 , - 4 )$
D) $( - 4,0 )$

Question 47

Solve the problem.
The value $\mathrm { V }$ , in dollars, of a shopkeeper's inventory software program is given by $\mathrm { V } = - 30 \mathrm { t } + 700$ , where $t$ is the number of years since the shopkeeper first bought the program. Graph the equation and then use the graph to estimate the value of the software after 5 years.

A) $\$ 540$

B) $\$ 550$

C) $\$ 560$

D) $\$ 700$

Question 48

Find the coordinates of the y-intercept and the coordinates of the x-intercept.

A) $( - 3 , - 7 ) , ( 0,0 )$
B) $( 0 , - 7 ) , ( - 3,0 )$
C) $( 0 , - 3 ) , ( - 7,0 )$
D) $( 0,0 ) , ( - 7 , - 3 )$

Question 49

Find the x- and y-intercepts for the equation. Then graph the equation.
$6 y-2 x=-10$

A) $\left( 0 , - \frac { 5 } { 3 } \right) , ( 5,0 )$

В) $\left( 0 , - \frac { 5 } { 3 } \right) , ( - 5,0 )$

Question 50

Solve the problem.
The value $\mathrm { V }$ , in dollars, of a shopkeeper's inventory software program is given by $\mathrm { V } = - 40 \mathrm { t } + 250$ , where $t$ is the number of years since the shopkeeper first bought the program. After how many years is the value of the software $\$ 10$ ?

A) $6 \mathrm { yr }$
B) $8 \mathrm { yr }$
C) $7 \mathrm { yr }$
D) $5 \mathrm { yr }$

Question 51

Find the coordinates of the y-intercept and the coordinates of the x-intercept.

A) $( 0 , - 6 ) , ( - 7,0 )$
В) $( - 6 , - 7 ) , ( 0,0 )$
C) $( 0 , - 7 ) , ( - 6,0 )$
D) $( 0,0 ) , ( - 7 , - 6 )$

Question 52

Find the coordinates of the y-intercept and the x-intercept, in that order.
$$x + y = - 7$$

A) $( - 2,0 ) ( - 5,0 )$
B) $( - 7 , - 5 ) ( - 2 , - 7 )$
C) $( - 7,0 ) ( 0 , - 7 )$
D) $( 0 , - 2 ) ( 0 , - 5 )$

Question 53

Find the coordinates of the y-intercept for the given equation.
$$y = \frac { 1 } { 2 } x - 5$$

A) $( - 5,0 )$
B) $( 5,0 )$
C) $\left( 0 , \frac { 1 } { 2 } \right)$
D) $( 0 , - 5 )$

Question 54

Find the x- and y-intercepts for the equation. Then graph the equation.
$$x + 3 y = 9$$

A) $( 9,0 ) , ( 0,3 )$

B) $( 3,0 ) , ( 0,9 )$

Question 55

Find the coordinates of the y-intercept and the x-intercept, in that order.
$$3 x - 5 y = 4$$

A) $\left( \frac { 4 } { 3 } , 0 \right) , \left( 0 , \frac { 4 } { 5 } \right)$
B) $( 1,0 ) , ( 0,9 )$
C) $\left( - \frac { 4 } { 5 } , 0 \right) , \left( 0 , \frac { 4 } { 3 } \right)$
D) $\left( \frac { 4 } { 3 } , 0 \right) , \left( 0 , - \frac { 4 } { 5 } \right)$

Question 56

Find the coordinates of the y-intercept and the x-intercept, in that order.
$$- 2 x + y = - 2$$

A) $( - 3,0 ) ( - 8,0 )$
В) $( - 2 , - 8 ) ( - 3 , - 2 )$
C) $( 0 , - 3 ) ( 0 , - 8 )$
D) $( 1,0 ) ( 0 , - 2 )$

Question 57

Find the coordinates of the y-intercept and the x-intercept, in that order.
$$2 x + y = 8$$

A) $( 4,0 ) ( 0,8 )$
B) $( 0,8 ) ( 0 , - 8 )$
C) $( 8 , - 8 ) ( 8,8 )$
D) $( 8,0 ) ( - 8,0 )$

Question 58

Find the coordinates of the y-intercept and the x-intercept, in that order.
$$5 y - 11 = 2 x$$

A) $( - 13,0 ) , ( 0,6 )$
B) $\left( \frac { 11 } { 5 } , 0 \right) , \left( 0 , - \frac { 11 } { 2 } \right)$
C) $\left( - \frac { 11 } { 2 } , 0 \right) , \left( 0 , \frac { 11 } { 5 } \right)$
D) $\left( \frac { 11 } { 2 } , 0 \right) , \left( 0 , - \frac { 11 } { 5 } \right)$

Question 59

Find the coordinates of the y-intercept and the x-intercept, in that order.
$$- 3 x - 2 y = 0$$

A) $( 0 , - 3 ) ( - 1,0 )$
В) $( - 1,0 ) ( - 3,0 )$
C) $( 0 , - 1 ) ( 0 , - 3 )$
D) $( 0,0 ) ( 0,0 )$

Question 60

Solve the problem.
The value $\mathrm { V }$ , in dollars, of a shopkeeper's inventory software program is given by $\mathrm { V } = - 20 \mathrm { t } + 450$ , where $t$ is the number of years since the shopkeeper first bought the program. Find the value of the software after 0 years, 6 years, and 10 years.

A) $\$ 450 , \$ 330$ , and $\$ 210$
B) $\$ 450 , \$ 330$ , and $\$ 250$
C) $\$ 430 , \$ 330$ , and $\$ 250$
D) $\$ 450 , \$ 570$ , and $\$ 250$

Question 61

Graph.
$$6 x + 23 = 0$$

A)

B)

C)

D)

Question 62

Find the slope of the line.

A) $- 3$
B) 3
C) $\frac { 1 } { 3 }$
D) $- \frac { 1 } { 3 }$

Question 63

Graph.
$4 y=10$
A)

B)

C)

D)

Question 64

Find the slope of the line.

A) 1
B) $- 1$
C) 6
D) $- 6$

Question 65

Write an equation for the graph.

A) $x = - 3$
B) $y = x - 3$
C) $y = - 3$
D) $y = x - 6$

Question 66

Graph.
$-4 x=-6$
A)

B)

C)

D)

Question 67

Find the slope of the line.

A) 3
B) 0
C) $\frac { 7 } { 6 }$
D) Undefined

Question 68

Graph.
$$x = - \frac { 3 } { 2 }$$

A)

B)

C)

D)

Question 69

Graph the line containing the given pair of points and find the slope.
$$( 2 , - 4 ) ( - 1,2 )$$

A) $- \frac { 1 } { 2 }$

B) 2

C) $\frac { 1 } { 2 }$

D) $- 2$

Question 70

Graph.
$$y = - \frac { 4 } { 3 }$$

A)

B)

C)

D)

Question 71

Graph the line containing the given pair of points and find the slope.
$$( - 9,0 ) ( - 12 , - 1 )$$

A) $- 3$

B) 3

C) $\frac { 1 } { 3 }$

D) $- \frac { 1 } { 3 }$

Question 72

Graph.
$x=-2$


A)

B)

C)

D)

Question 73

Find the x- and y-intercepts for the equation. Then graph the equation.
$$2 x - 4 y = 12$$

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

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

Question 74

Write an equation for the graph.

A) $x = - 3$
B) $y = - 3$
C) $y = x - 6$
D) $y = x - 3$

Question 75

Graph.
$$y = 2$$

A)

B)

C)

D)

Question 76

Find the slope of the line.

A) 1
B) $- 7$
C) 7
D) $- 1$

Question 77

Find the x- and y-intercepts for the equation. Then graph the equation.
$5 x-30 y=0$

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

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

Question 78

Graph the line containing the given pair of points and find the slope.
$$( 1,5 ) ( 0,0 )$$

A) $- \frac { 1 } { 5 }$

B) 5

C) $\frac { 1 } { 5 }$

D) $- 5$

Question 79

Find the slope of the line.

A) $- 1$
B) Undefined
C) 0
D) $\frac { 3 } { 2 }$

Question 80

Find the slope of the line.

A) $- \frac { 1 } { 2 }$
B) $\frac { 1 } { 2 }$
C) 2
D) $- 2$