Deck 3: Linear Equations, Graphs, and Functions

Question 1

The graph shows sales in thousands of dollars for 1989 and 1990. Use it to answer the question


-If the ordered pair $(x, y)$ represents a point on the graph, what does $x$ represent? What does $y$ represent?

A) $y$ represents the month; $x$ represents the sales in thousands of dollars.
B) $x$ represents the month; $y$ represents the sales in thousands of dollars.
C) $x$ represents the year 2006; y represents the sales in thousands of dollars
D) $x$ represents the year 2006; y represents the year 2007 .

Answer 1

$x$ represents the month; $y$ represents the sales in thousands of dollars.

Question 2

The graph shows sales in thousands of dollars for 1989 and 1990. Use it to answer the question


-Estimate the sales in June 2006.

A) about $\$ 64$ thousand
B) about $\$ 48$ thousand
C) about $\$ 52$ thousand
D) about $\$ 50$ thousand

Answer 2

about $\$ 50$ thousand

Question 3

The graph shows sales in thousands of dollars for 1989 and 1990. Use it to answer the question


-Write an ordered pair $(x, y)$ that gives approximately the sales in June 2006.

A) (June, 50)
B) $(6,50)$
C) $(2006,50)$
D) $(50,6)$

Answer 3

$(6,50)$

Question 4

The graph shows sales in thousands of dollars for 1989 and 1990. Use it to answer the question

-What does the ordered pair $(10,48)$ for 2006 mean in the context of this graph?

Question 5

The graph shows sales in thousands of dollars for 1989 and 1990. Use it to answer the question


-Which month in 2006 had the lowest sales?

A) Month 8
B) Month 3
C) Month 2
D) Month 6

Question 6

The graph shows sales in thousands of dollars for 1989 and 1990. Use it to answer the question


-Which month in 2007 had the highest sales?

A) Month 5
B) Month 12
C) Month 3
D) Month 6

Question 7

The graph shows sales in thousands of dollars for 1989 and 1990. Use it to answer the question


-What month in 2006 had the highest sales?

A) Month 2
B) Month 12
C) Month 3
D) Month 5

Question 8

The graph shows sales in thousands of dollars for 1989 and 1990. Use it to answer the question


-What month in 2007 had the lowest sales?

A) Month 2
B) Month 5
C) Month 12
D) Month 3

Question 9

Name the quadrant, if any, in which the point is located.

- $(7,17)$

A) III
B) I
C) II
D) None

Question 10

Name the quadrant, if any, in which the point is located.

- $(-20,9)$

A) I
B) None
C) II
D) III

Question 11

Name the quadrant, if any, in which the point is located.

- $(-11,-5)$

A) III
B) II
C) None
D) IV

Question 12

Name the quadrant, if any, in which the point is located.

- $(10,-13)$

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

Question 13

Name the quadrant, if any, in which the point is located.

- $(-12,0)$

A) II
B) IV
C) None
D) III

Question 14

Name the quadrant, if any, in which the point is located.

- $(0,-17)$

A) II
B) IV
C) None
D) III

Question 15

Plot the point on the rectangular coordinate system provided. Write the corresponding letter as your answer.


- $(0,2)$

A) $\mathrm{F}$
B) $\mathrm{K}$
C) $\mathrm{C}$
D) B

Question 16

Plot the point on the rectangular coordinate system provided. Write the corresponding letter as your answer.


- $(-5,-4)$

A) I
B) A
C) $\mathrm{L}$
D) $G$

Question 17

Plot the point on the rectangular coordinate system provided. Write the corresponding letter as your answer.


- $(-3,4)$

A) $B$
B) $\mathrm{K}$
C) $\mathrm{A}$
D) $\mathrm{F}$

Question 18

Plot the point on the rectangular coordinate system provided. Write the corresponding letter as your answer.


- $(-3,0)$

A) $\mathrm{F}$
B) $\mathrm{C}$
C) J
D) G

Question 19

Plot the point on the rectangular coordinate system provided. Write the corresponding letter as your answer.


- $(3,5)$

A) D
B) $\mathrm{K}$
C) $\mathrm{L}$
D) I

Question 20

Plot the point on the rectangular coordinate system provided. Write the corresponding letter as your answer.


- $(4,3)$

A) C
B) $\mathrm{D}$
C) $\mathrm{K}$
D) $\mathrm{E}$

Question 21

Plot the point on the rectangular coordinate system provided. Write the corresponding letter as your answer.


- $(0,-3)$

A) C
B) I
C) $\mathrm{G}$
D) J

Question 22

Plot the point on the rectangular coordinate system provided. Write the corresponding letter as your answer.


- $(2,0)$

A) C
B) F
C) $\mathrm{K}$
D) B

Question 23

Plot the point on the rectangular coordinate system provided. Write the corresponding letter as your answer.


- $(4,-5)$

A) $\mathrm{L}$
B) $\mathrm{A}$
C) $\mathrm{F}$
D) $\mathrm{K}$

Question 24

Complete the table for the equation.

- $x+y=6$

A) $4 ; 6 ; 0$
B) $8 ; 0 ; 6$
C) $2 ; 0 ; 6$
D) $2 ; 2 ; 6$

Question 25

Complete the table for the equation.

- $y=-x+3$

A) $-5 ; 0 ; 3$
B) $6 ; 0 ; 3$
C) $6 ; 0 ; 0$
D) $-5 ; 6 ; 3$

Question 26

Complete the table for the equation.

- $4 x+y=7$

A) $7 ;-21 ;-21$
B) $-9 ;-21 ; 7$
C) $-9 ;-21 ;-21$
D) $7 ; 7 ; 7$

Question 27

Complete the table for the equation.

- $y+3 x=-16$

A) $5 ;-16 ;-16$
B) $-7 ;-16 ;-16$
C) $5 ;-32 ; 32$
D) $5 ;-16 ; 0$

Question 28

Complete the table for the equation.

- $y=-9 x-65$

A) $7 ; 0 ; 1$
B) $-8 ;-65 ; 1$
C) $7 ;-65 ; 1$
D) $7 ;-79 ; 1$

Question 29

Complete the table for the equation.

- $x-4 y=-16$

A) $-3 ;-4 ;-5$
B) $0 ;-4 ;-8$
C) $5 ; 4 ; 3$
D) $3 ; 4 ; 5$

Question 30

Complete the table for the equation.

- $-6 x+2 y=8$

A) $0 ; 10 ;-2$
B) $0 ;-10 ;-2$
C) $0 ; 2 ;-10$
D) $0 ;-2 ; 10$

Question 31

Graph the equation by determining the missing values needed to plot the ordered pairs.

- $y+x=3 ;(1, ),(3, ),(2, )$

A)
B)
C)
D)

Question 32

Graph the equation by determining the missing values needed to plot the ordered pairs.

- $y - x=1 ;(3, \quad),(\quad ,8),(4, \quad)$

A)
B)
C)
D)

Question 33

Graph the equation by determining the missing values needed to plot the ordered pairs.

- $x-2 y=-8 ;(0, \quad),( \quad ,0),(3, \quad),( \quad ,3)$

A)
B)
C)
D)

Question 34

Graph the equation by determining the missing values needed to plot the ordered pairs.

- $4 x-5 y=-20 ;(0, \quad),( \quad,0),(-1, \quad),( \quad,2)$

A)

B)

C)
D)

Question 35

Find the $x$ - and $y$ -intercepts. Then graph the equation.

- $10y - 2 x= -4$

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


B) $(2,0) ;\biggl(0,-\frac{2}{5}\biggl)$


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

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

Question 36

Find the $x$ - and $y$ -intercepts. Then graph the equation.

- $-6 x-12 y=24$

A) $(-2,0) ;(0,4)$


B) $(-2,0) ;(0,-4)$


C) $(-4,0) ;(0,-2)$


D) $(4,0) ;(0,-2)$

Question 37

Find the $x$ - and $y$ -intercepts. Then graph the equation.

- $y=-2$

A) None; $(0,-2)$


B) $(-2,0)$ ; none


C) None; $(0,-2)$


D) $(-2,0)$ ; none

Question 38

Find the $x$ - and $y$ -intercepts. Then graph the equation.

- $2 x - 4 y=8$

A) $(-2,0) ;(0,4)$


B) $(-4,0) ;(0,4)$


C) $(-2,0) ;(0,4)$


D) $(4,0) ;(0,-2)$

Question 39

Find the $x$ - and $y$ -intercepts. Then graph the equation.

- $3x -18 y=0$

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


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


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


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

Question 40

Find the $x$ - and $y$ -intercepts. Then graph the equation.

- $\frac{11}{5} x+\frac{1}{5} y=1$

A) $\left(-\frac{5}{11}, 0\right) ;(0,5)$


B) $\left(\frac{5}{11}, 0\right) ;(0,5)$


C) $\left(-\frac{5}{11}, 0\right) ;(0,-5)$


D) $\left(\frac{5}{11}, 0\right) ;(0,-5)$

Question 41

Find the $x$ - and $y$ -intercepts. Then graph the equation.

- $2 y=\frac{3}{5} x$

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


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


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

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

Question 42

Find the $x$ - and $y$ -intercepts. Then graph the equation.

- $x=5$

A) $(5,0)$ ; none


B) None ; $(0,5)$


C) None ; $(0,5)$


D) $(5,0)$ ; none

Question 43

Find the midpoint of the segment with the given endpoints.

- $(8,4)$ and $(7,9)$

A) $(1,-5)$
B) $\biggl(\frac{15}{2}, \frac{13}{2}\biggl)$
C) $\biggl(\frac{1}{2},-\frac{5}{2}\biggl)$
D) $(15,13)$

Question 44

Find the midpoint of the segment with the given endpoints.

- $(1,-9)$ and $(-5,6)$

A) $(6,-15)$
B) $\biggl(-2,-\frac{3}{2}\biggl)$
C) $\biggl(3,-\frac{15}{2}\biggl)$
D) $(-4,-3)$

Question 45

Find the midpoint of the segment with the given endpoints.

- $(-1,0)$ and $(9,8)$

A) $(4,4)$
B) $(-10,-8)$
C) $(8,8)$
D) $(-5,-4)$

Question 46

Find the midpoint of the segment with the given endpoints.

- $(2,-2)$ and $(7,-6)$

A) $(-5,4)$
B) $(9,-8)$
C) $\biggl(\frac{9}{2},-4\biggl)$
D) $\biggl(-\frac{5}{2}, 2\biggl)$

Question 47

Find the midpoint of the segment with the given endpoints.

- $\biggl(-\frac{7}{2},-\frac{9}{2}\biggl)$ and $\biggl(\frac{5}{2}, \frac{11}{2}\biggl)$

A) $(4,4)$
B) $(-3,-5)$
C) $\biggl(-\frac{1}{2}, \frac{1}{2}\biggl)$
D) $(144,400)$

Question 48

Find the midpoint of the segment with the given endpoints.

- $(-5.6,0.6)$ and $(-6.6,6.4)$

A) $(1,-5.8)$
B) $(-6.1,3.5)$
C) $(0.5,-2.9)$
D) $(-12.2,7)$

Question 49

Suppose that segment $P Q$ has the given coordinates for one endpoint $P$ and for its midpoint $M$ . Find the coordinates of the other endpoint $Q$ .

- $P(5,5)$ and $M\biggl(\frac{9}{2}, \frac{9}{2}\biggl)$

A) $Q(9,9)$
B) $\mathrm{Q}\biggl(\frac{1}{2}, \frac{1}{2}\biggl)$
C) $\mathrm{Q}(4,4)$
D) $Q(1,1)$

Question 50

Suppose that segment $P Q$ has the given coordinates for one endpoint $P$ and for its midpoint $M$ . Find the coordinates of the other endpoint $Q$ .

- $P(0,-9)$ and $M(-3,-4)$

A) $Q(3,-5)$
B) $Q(-6,-8)$
C) $Q(-6,1)$
D) $Q(6,-10)$

Question 51

Suppose that segment $P Q$ has the given coordinates for one endpoint $P$ and for its midpoint $M$ . Find the coordinates of the other endpoint $Q$ .

- $\mathrm{P}(4,8)$ and $M\biggl(\frac{1}{2}, \frac{5}{2}\biggl)$

A) $Q(-3,-3)$
B) $Q(1,5)$
C) $Q\biggl(-\frac{7}{2},-\frac{11}{2}\biggl)$
D) $Q(-7,-11)$

Question 52

Suppose that segment $P Q$ has the given coordinates for one endpoint $P$ and for its midpoint $M$ . Find the coordinates of the other endpoint $Q$ .

- $P(-9,-9)$ and $M(0,-7)$

A) $Q(9,2)$
B) $Q(18,4)$
C) $Q(9,-5)$
D) $Q(0,-14)$

Question 53

Suppose that segment $P Q$ has the given coordinates for one endpoint $P$ and for its midpoint $M$ . Find the coordinates of the other endpoint $Q$ .

- $\mathrm{P}\biggl(\frac{9}{2},-\frac{5}{2}\biggl)$ and $M\biggl(1, \frac{1}{2}\biggl)$

A) $Q(16,4)$
B) $Q\biggl(-\frac{5}{2}, \frac{7}{2}\biggl)$
C) $Q\biggl(\frac{7}{2},-3\biggl)$
D) $Q(196,144)$

Question 54

Suppose that segment $P Q$ has the given coordinates for one endpoint $P$ and for its midpoint $M$ . Find the coordinates of the other endpoint $Q$ .

- $P(1.1,6.8)$ and $M(-3.35,7.3)$

A) $Q(-7.8,7.8)$
B) $Q(4.45,-0.5)$
C) $Q(8.9,-1)$
D) $Q(-6.7,14.6)$

Question 55

Solve the problem.

-The graphing calculator screen shows the graph of one of the equations below. Which equation is it?

A) $y=3 x+3$
B) $y+3 x=3$
C) $y-3 x=15$
D) $y+3 x=15$

Question 56

Solve the problem.

-The graphing calculator screen shows the graph of one of the equations below. Which equation is it?

A) $y-4 x=-5$
B) $y=-4 x+3$
C) $y-4 x=3$
D) $y+4 x=-5$

Question 57

Solve the problem.

-The graphing calculator screen shows the graph of one of the equations below. Which equation is it?

A) $x+y=5$
B) $x-y=-1$
C) $y-x=1$
D) $y=3$

Question 58

Solve the problem.

-The graphing calculator screens show the graph of one of the equations below. Which equation is it?

A) $-3 x+4 y=12$
B) $3 x+4 y=12$
C) $3 x-4 y=12$
D) $3 x-4 y=-12$

Question 59

Solve the problem.

-The graphing calculator screens show the graph of one of the equations below. Which equation is it?

A) $-2 x+3 y=-6$
B) $2 x-3 y=6$
C) $3 x-2 y=-6$
D) $-2 x+3 y=6$

Question 60

Solve the problem.

-The table of ordered pairs was generated by a graphing calculator with a table feature. Which equation corresponds to this table of values?

A) $y_{1}=-4 x+5$
B) $\mathrm{y}_{1}=4 \mathrm{x}-5$
C) $\mathrm{y}_{1}=4 \mathrm{x}+5$
D) $y_{1}=-4 x-5$

Question 61

Solve the problem.

-The table of ordered pairs was generated by a graphing calculator with a table feature. Which equation corresponds to this table of values?

A) $y_{1}=\frac{1}{2} x+3$
B) $y_{1}=-\frac{1}{2} x-3$
C) $y_{1}=-\frac{1}{2} x+3$
D) $\mathrm{y}_{1}=\frac{1}{2} \mathrm{x}-3$

Question 62

Solve the problem.

-Suppose that it has been determined that if 100 of a certain fish are introduced into a pond with certain environmental conditions, then in $x$ months, there will be $y=4.35 x+100$ fish in the pond. A portion of the graph of this equation is shown on the accompanying screen, along with the coordinates of a point on the line. How can this point be interpreted in the context of the model?

A) It means that there could be between 5 and 120 fish in the pond at a certain time
B) It means that in 119.6 months, there should be approximately 5 fish in the pond
C) It means that there will be fish in the pond in 4.5 months and in 119.6 months
D) It means that in 4.5 months, there should be approximately 120 fish in the pond

Question 63

Solve the problem.

-Suppose that the speed at which an experienced person can paddle a canoe upstream is approximated by $y=-2.5 x+15(0<x<6)$ , where $x$ is the number of hours paddled and $y$ is the speed of the canoe in miles per hour. A portion of the graph of this equation is shown on the accompanying screen, along with the coordinates of a point on the line. How can this point be interpreted in the context of the model?

A) It means that after 7.5 hours of paddling, the canoe is traveling at a speed of 3 miles per hour.
B) It means that after 3 hours of paddling, the canoe is traveling at a speed of 7.5 miles per hour.
C) It means that an experienced person can paddle between 3 and 7.5 hours.
D) It means that the canoe can travel at a speed of between 3 and 7.5 miles per hour

Question 64

Solve the problem.

-The winning speeds for the Grayslake 250 race from 1980-1992 are approximated by the linear equation $y=2.503 x+198.729$ . In the model, $x=0$ corresponds to $1980, x=1$ to 1981 , and so on. A portion of the graph of the equation is shown on the accompanying screen, along with the coordinates of a point on the line. How can this point be interpreted in the context of the model?

A) It means that in the year 1990, the winning speed was approximately 224 miles per hour.
B) It means that the winning speed in the year 1990 will be the same as in the year 2203.
C) It means that 10 years from now, the winning speed will be approximately 224 miles per hour.
D) It means that the winning speed was between 10 and 224 miles per hour.

Question 65

The point with coordinates $(0,0)$ is called the

Question 66

For any value $x$ , the point $(x, 0)$ lies on the _ axis.

Question 67

To find the $y$ -intercept of a line we let $\_=0$ and solve for__

Question 68

The equation _ $=6$ has a vertical line as its graph.

Question 69

To graph a straight line, we must find a minimum of _ points.

Question 70

Determine the quadrants in which the given point ( $x, y)$ may lie when $x y>0$ .

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

Question 71

Determine the quadrants in which the given point $(x, y)$ may lie when $x>0$ .

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

Question 72

Find the slope.

- $m=\frac{13-3}{7-5}$

A) -5
B) 8
C) 5
D) 12

Question 73

Find the slope.

- $m=\frac{2-4}{-3-1}$

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

Question 74

Find the slope.

- $\mathrm{m}=\frac{5-(-5)}{-7-(-4)}$

A) $\frac{10}{3}$
B) $-\frac{10}{3}$
C) 0
D) $-\frac{10}{9}$

Question 75

Find the slope.

- $\mathrm{m}=\frac{-10-(-10)}{7-4}$

A) $-\frac{20}{3}$
B) $\frac{20}{3}$
C) Undefined
D) 0

Question 76

Find the slope.

- $\mathrm{m}=\frac{8-4}{-5-(-5)}$

A) $-\frac{2}{5}$
B) Undefined
C) 0
D) 4

Question 77

Find the slope.

- $\mathrm{m}=\frac{6-(-3)}{1-(-3)}$

A) $\frac{9}{10}$
B) $\frac{3}{4}$
C) $-\frac{9}{4}$
D) $\frac{9}{4}$

Question 78

Find the slope.

- $m=\frac{4-2}{9-4}$

A) 0
B) $\frac{2}{5}$
C) Undefined
D) $\frac{6}{5}$

Question 79

Find the slope.

- $\mathrm{m}=\frac{5-(-9)}{9-(-4)}$

A) $-\frac{4}{5}$
B) Undefined
C) $\frac{14}{13}$
D) 0

Question 80

Find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line through the points rises from left to right, falls from left to right, is horizontal, or is vertical.

- $(-3,-5)$ and $(4,-4)$

A) 7; rises
B) $-\frac{1}{7}$ ; falls
C) $\frac{1}{7}$ ; rises
D) - 7; falls