Deck 3: Graphs, Linear Equations, and Inequalities in Two Variables; Functions From Campus to Careers: Physical Therapis

Question 1

The point with coordinates x = -1 and y = 19 lies in the first quadrant.

Answer 1

False

Question 2

The ordered pair (3, -4)satisfies the equation y = $-$ 3 x + 5.

Answer 2

True

Question 3

Complete the solution of equation. $$y = \frac { 1 } { 7 } x - 3 , \quad ( 7 , ? )$$

A)2
B)-2
C)46
D)-46

Answer 3

-2

Question 4

The charges for renting a CD are shown in the graph. Find the charge if the CD is kept for 7 days.

A)$7
B)$6
C)$3
D)$5
E)$4

Question 5

A student plotted three points that belong to the graph of a certain equation. Is this equation linear or nonlinear?

A)Nonlinear
B)Linear

Question 6

Refer to the line graph. At what times (A, B, C or D)do you find the following conditions: runner 1 running and runner 2 running?

A)A and C
B)A and D
C)A only
D)A and B
E)B and C

Question 7

Plot the points on a rectangular coordinate system, and determine if the points fall in a straight line. $$( - 14 ) , ( - 4,1 ) , ( - 5,0 ) , ( - 6 , - 1 )$$

A) Yes
B) No
C) No
D) Yes

Question 8

To plot the point with coordinates (38,-83)we:

A)start at the origin and move 38 units to the left and then move 83 units up.
B)start at the origin and move 38 units to the left and then move 83 units down.
C)start at (1,1)and move 38 units to the right and then move 83 units down.
D)start at the origin and move 38 units to the right and then move 83 units up.
E)start at the origin and move 38 units to the right and then move 83 units down.

Question 9

Scoliosis is a lateral curvature of the spine that can be more easily detected when a grid is superimposed over an X ray. Select the ordered pair that is not one of the "center points" of the labeled vertebrae. Note that T3 means the third thoracic vertebra, L4 means the fourth lumbar vertebra, and so on.

A) $( - 1 , - 5 )$
B) $( - 2,3 )$
C)(3,10)
D)(3,16)
E)(0,0)

Question 10

Refer to the line graph. In approximately what year did miners begin to earn more than construction workers?

A)in 1984
B)in 1982
C)in 1988
D)in 1985
E)in 1990

Question 11

The graph below shows the value y (in thousands of dollars)of a car that is x years old. Is it true that the value of a car that is 3 years old is $6,000?

Question 12

Complete the solution of equation. $$y = 4 x - 3 , \quad ( 2 , ? )$$

A)14
B)11
C)8
D)7

Question 13

The graph below gives the heart rate of a woman before, during and after an aerobic workout. Is it true that her heart rate 40 minutes after beginning her workout was 150?

Question 14

Complete the solution of equation. $$y = - 5 x + 3 , \quad ( - 2 , ? )$$

A)-17
B)13
C)10
D)-2

Question 15

To correct her swing, a golfer is videotaped and then has her image displayed on a computer monitor so that it can be analyzed by a golf pro. Refer to the illustration to find the -coordinate of the highlighted point where the -coordinate is -5. __________ units

Question 16

The graph shows the relationship between the percent P of those surveyed who rated their senator's job performance as satisfactory or better and the time t she had been in office. When did her job performance rating reach a maximum? __________ months after election

Question 17

The charges for renting a video are shown in the graph. Find the charge if the video is kept for 6 days.

A)$5
B)$9
C)$6
D)$8
E)$7

Question 18

The graph shown gives the first-class postage rates in the year 1999 for mailing items weighing up to 5 ounces. According to the graph, which of the statements is incorrect? Weight (oz)and Postage Rate (cents)

A)The postage cost for mailing a 2-ounce letter is 55 cents .
B)The heaviest letter that could be mailed for 80 cents first class weighs 2 ounces.
C)The postage cost for mailing a 1-ounce letter is 33 cents.
D)The difference in postage for a 3.16-ounce letter and a 4.37-ounce letter is 20 cents .
E)The postage cost for mailing a 4-ounce letter is $1.00.

Question 19

The graph below shows how the path of a stream of water changes when the hose is held at two different angles. The stream shot up higher at the $80 ^ { \circ }$ angle.

Question 20

The graph, given below, shows the relationship between the market value v of a house and the time t since it was purchased. When did the value of the house reach its lowest point? __________ years after purchase

Question 21

Graph the equation. $$x + 4 = 0$$

A)
B)
C)
D)
E)

Question 22

Find the power of variables x and y to say whether the equation is linear or nonlinear. $$- x ^ { 3 } + 3 y ^ { 5 } = 1$$

A)0; 0; linear
B)3; 5; linear
C)3; 5; nonlinear
D)1; 1; nonlinear

Question 23

Write the rate as a unit rate. $28$ trips every $4$ months

A) $7$ trips per month
B) $4$ trips per month
C) $28$ trips per month
D) $8$ trips per month
E) $6$ trips per month

Question 24

Graph the equation using the intercept method. Label the intercepts on the graph. $$3 x + 4 y - 8 = 0$$

A)
B)
C)
D)
E)

Question 25

The cost ( c )of playing an online computer game for a time ( t )in hours is given by the equation c = 3 t + 5. Label the horizontal axis t and the vertical axis c , and graph the equation for nonnegative values of t .

A)
B)
C)
D)
E)

Question 26

Graph the equation using the intercept method. Label the intercepts on the graph. $$2 y = 4 x - 6$$

A)
B)
C)
D)
E)

Question 27

Find the slope of the line determined by this pair of points. (4, 6), (14, 13)

A) $\frac { 7 } { 10 }$
B) $7$
C) $- \frac { 7 } { 10 }$
D) $\frac { 10 } { 7 }$
E) $- \frac { 10 } { 7 }$

Question 28

Find the slope of the line by finding the coordinates of two points on it. 10 x + 3 y = 7

A) $- \frac { 3 } { 10 }$
B) $\frac { 10 } { 3 }$
C) $- \frac { 1 } { 3 }$
D) $- \frac { 10 } { 3 }$
E) $- \frac { 1 } { 10 }$

Question 29

Graph the equation using the intercept method. Label the intercepts on the graph. $$2 x + 3 y = 6$$

A)
B)
C)
D)
E)

Question 30

Graph the equation. $$y = 3 x - 4$$

A)
B)
C)
D)
E)

Question 31

Find the slope of the line determined by the equation. $$x = \frac { 5 - y } { 6 }$$

A) $m = - \frac { 5 } { 6 }$
B) $m = - 6$
C) $m = \frac { 5 } { 6 }$
D) $m = 6$
E) $m = - \frac { 1 } { 6 }$

Question 32

Graph the equation. $$- 3 y = 3$$

A)
B)
C)
D)
E)

Question 33

Graph the linear equation. $$3 x = - 2$$

A)
B)
C)
D)
E)

Question 34

Determine which of the ordered pairs satisfy the given equation and then graph the equation by plotting the points that satisfy the equation. $$y = - x + 4 ; ( 1,3 ) , ( 0,4 ) , ( 2 , - 5 ) , ( - 2,6 ) , ( - 1,5 )$$

A)
B)
C)
D)
E)

Question 35

The graph below gives the heart rate of a woman before, during, and after an aerobic workout. Use the graph to answer the question. What was her heart rate before beginning the workout? __________ beats\min

Question 36

Find the slope of the line by finding the coordinates of two points on it. y = 2 x

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

Question 37

Write the rate as a unit rate. $220$ presents for $55$ children

A) $3$ presents per child
B) $5$ presents per child
C) $6$ presents per child
D) $7$ presents per child
E) $4$ presents per child

Question 38

Solve the equation for y and then graph it. $$2 x - y = - 3$$

A)
B)
C)
D)
E)

Question 39

The equation $F = \frac { 9 } { 5 } C + 31$ can be used to convert from degrees in Celsius to degrees in Fahrenheit. Identify the graph of the equation.

A)
B)
C)
D)
E)

Question 40

Write each rate as a unit rate. $3,891,300$ people living in $10,500$ square

A) $370.6$ people per square mi
B) $36.6$ people per square mi
C) $355.6$ people per square mi
D) $388.6$ people per square mi
E) $390.6$ people per square mi

Question 41

Find the slope and the y -intercept of the line determined by the given equation. $$5 x = 2 y - 8$$

A)slope: $- \frac { 2 } { 5 }$ ; y -intercept: $( 0,4 )$
B)slope: $\frac { 2 } { 5 }$ ; y -intercept: $( 0,4 )$
C)slope: $\frac { 5 } { 2 }$ ; y -intercept: $( 0,4 )$
D)slope: $- \frac { 5 } { 2 }$ ; y -intercept: $( 0 , - 4 )$
E)slope: $\frac { 5 } { 2 }$ ; y -intercept: $( 0 , - 4 )$

Question 42

Find the slope of the line determined by this pair of points. $( m , 0 ) , ( 0 , n )$

A) $- \frac { n } { m }$
B) $\frac { m } { n }$
C) $- \frac { m } { n }$
D) $\frac { n } { m }$
E)undefined

Question 44

Change the equation to slope-intercept form. $2 x - 11 y = 1$

A) $x = \frac { 11 } { 2 } y - \frac { 1 } { 11 }$
B) $y = 2 x - 1$
C) $y = \frac { 11 } { 2 } - \frac { 1 } { 11 } x$
D) $y = 2 x - 11$
E) $y = \frac { 2 } { 11 } x - \frac { 1 } { 11 }$

Question 45

Solve $7 x + 8 y = 8$ for y.

A) $8 y = - 7 x + 8$
B) $y = \frac { 7 } { 8 } x + 1$
C) $y = - 8 x + 1$
D) $y = - \frac { 7 } { 8 } x + 1$

Question 46

Tell whether the lines with the given slopes are parallel, perpendicular, or neither. $$m _ { 1 } = 5 , m _ { 2 } = - \frac { 1 } { 4 }$$

A)neither
B)parallel
C)perpendicular

Question 47

Find the slope of the line determined by this pair of points. (3, -7), (1, -7)slope = __________

Question 48

For the following pair of equations, predict whether they represent parallel lines, perpendicular lines, or lines that intersect but are not perpendicular. 5.4 x + 2.4 y = 6.4 and 2.4 x - 5.4 y = 1.4

A)parallel lines
B)lines that intersect but are not perpendicular
C)perpendicular lines

Question 49

Graph the line that passes through the given point and has the given slope. $( 3,2 ) , m = \frac { 5 } { 3 }$

A)
B)
C)
D)
E)

Question 50

Determine the y -intercept of the line represented by the given equation. $$- y = \frac { 7 } { 4 } x + \frac { 4 } { 3 }$$

A) $b = - \frac { 3 } { 4 }$
B) $b = - \frac { 7 } { 4 }$
C) $b = \frac { 7 } { 4 }$
D) $b = \frac { 4 } { 3 }$
E) $b = - \frac { 4 } { 3 }$

Question 51

Determine if the slope of the line is positive, negative, zero or undefined.

A)zero
B)undefined
C)negative
D)positive
E)The graph isn't a line.

Question 52

Find the slope of the line passing through the given points: A (8, 4); B (8, 7)

A) $m = 3$
B) $\frac { 1 } { 3 }$
C) $m = - \frac { 1 } { 3 }$
D) $m = 0$
E)m = undefined

Question 53

Graph the linear equation. $x + y = 5$

A)
B)
C)
D)
E)

Question 54

Graph the linear equation. $4 x - y = 5$

A)
B)
C)
D)
E)

Question 55

Find the slope of the line determined by this pair of points. (1.8, 6.3), (5.8, 9.3)

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

Question 56

Find the slope of a vertical line. Enter the value (as a whole number or simplified fraction). If the slope is undefined, enter undefined . m = __________

Question 57

Find the slope of the line by finding the coordinates of two points on it. y = 9 x

A) $\frac { 1 } { 9 }$
B) $9$
C) $0$
D) $- \frac { 1 } { 9 }$
E) $- 9$

Question 59

Determine if the slopes of these lines are positive, negative, zero or undefined.

A)blue line: positive; pink line: negative,
B)blue line undefined; pink line: positive
C)blue line: positive; pink line: positive
D)blue line: negative; pink line: positive
E)The graph isn't a line.

Question 60

Tell whether the graphs of the following pair of equations are parallel , perpendicular , or neither . $$y = 5 x - 15 , y = \frac { 1 } { 5 } x + 22$$

A)neither
B)parallel
C)perpendicular

Question 61

Use the point-slope form to write an equation of the line with the slope $-$ 6 and that passes through the point ( $-$ 9, 2). Then write your result in slope-intercept form.

A) $y = - 6 x - 51$
B) $y = - 6 x - 50$
C) $y = - 6 x - 52$
D) $y = 6 x - 51$
E) $y = 6 x - 52$

Question 62

Find the slope and the y -intercept of the line of the equation. y = -0.00017 x 0.0017

Question 63

Find the equation of the line that contains the two given points. Express the equation in the form , where A , B , and C are integers.

Question 64

Find the equation of the line that contains the two given points. $( 3,1 ) , ( 10,4 )$

A)7 y + 3 x = -2
B)3 x - 7 y = -2
C)7 y - 3 x = -2
D)7 y - 3 x = 16
E)7 y + 3 x = 16

Question 65

If the rise of the roof shown in the illustration is 5 feet, and the run is 9 feet, find the pitch of the roof.

A) $- \frac { 5 } { 9 }$
B)45
C) $\frac { 5 } { 9 }$
D)14
E) $\frac { 9 } { 5 }$

Question 66

Use the point-slope form to write an equation of the line with the slope $- \frac { 3 } { 5 }$ and that passes through the point $( - 2 , - 6 )$ .

A) $y - 2 = - \frac { 3 } { 5 } ( x + 6 )$
B) $y + 2 = - \frac { 3 } { 5 } ( x + 6 )$
C) $y - 6 = - \frac { 3 } { 5 } ( x + 2 )$
D) $y + 6 = - \frac { 3 } { 5 } ( x + 2 )$
E) $y + 6 = \frac { 3 } { 5 } ( x + 2 )$

Question 67

The equation of the horizontal line passing through (10, -9)is x = -9.

Question 68

Use the point-slope form to write an equation of the line with the slope $-$ 8 and that passes through the point ( $-$ 2, 4). Then write your result in slope-intercept form.

A) $y = - 8 x - 14$
B) $y = - 8 x - 10$
C) $y = - 8 x - 12$
D) $y = 8 x - 14$
E) $y = 8 x - 12$

Question 69

The height (in inches)of a human is almost linearly related to his\her body weight (in pounds). For example, a 5'2'' tall person would weight around 118 lb; and a 5'9'' tall person would weight around 139 lb. Can you predict how tall could be a person whose weight is 181 lb?

A)6'11''
B)11'6''
C)10'6''
D)6'10''

Question 70

Find the slope m and the y -intercept of the line y = 2.663 + 8.415 x

A)m = 8.415, y int = 2.663
B)m = 2.663; y int = 8.415
C)m = -8.415, y int = 2.663
D)m = 8.415, y int = 0

Question 71

The grade of a highway up a hill is 27%. How much change in horizontal distance is there if the vertical height of the hill is 250 feet? Express the answer to the nearest foot.

A)945 ft
B)926 ft
C)826 ft
D)936 ft
E)901 ft

Question 72

Use the point-slope form to write an equation of the line with the slope 8 and that passes through the point (1, 4).

A)y + 1 = 8( x $-$ 4)
B)y $-$ 4 = 8( x + 1)
C)y + 4 = 8( x $-$ 1)
D)y $-$ 4 = 8( x $-$ 1)
E)y $-$ 1 = 8( x $-$ 4)

Question 73

Determine whether the graphs of y = 3 x - 7 and y = $\frac{6}{7}$ x - 2 of are parallel, perpendicular, or neither.

A)parallel
B)neither parallel, nor perpendicular
C)perpedicular

Question 74

The equation of the vertical line that passes through (-9, -10)is x = -9.

Question 75

If the ratio of rise to run is to be $\frac { 1 } { 3 }$ for some stairs and the measure of the run is 22 centimeters, find the measure of the rise to the nearest centimeter.

A)66 cm
B)6 cm
C)7 cm
D)17 cm
E)22 cm

Question 76

Find the equation of the line that contains the two given points. $( - 8,0 ) , ( 0 , - 3 )$

A)8 y + 3 x = -24
B)8 y + 3 x = 24
C)8 y - 3 x = -3
D)8 y - 3 x = -24
E)8 y - 3 x = 24

Question 77

Write an equation of a horizontal line passing through (-2, 4)and an equation of a vertical line passing through (4, -3).Graph both lines.

A)
B)
C)
D)

Question 78

An automated production line uses distilled water at a rate of 700 gallons every 4 hours to make toothpaste. After the line had run for 6 hours, planners noted that 1700 gallons of distilled water remained in the storage tank. Find the number of gallons of distilled water in the storage tank when the production line began.

A)9200 gallons
B)4800 gallons
C)2750 gallons
D)6800 gallons
E)none of these

Question 79

Find the slope of the line of the equation. y = 0.4 x 2

Question 80

You and your friends each eat 2 slices of pizza for dinner, there are 8 slices in a pie, and the delivery fee is $5. You must tip 10% on the pizza order but not on the delivery fee. Express the total cost in an expression.

A)y = 2 x + 5
B)y = 2.2 x + 5
C)y = 0.2 x + 5
D)y = 2 x