Deck 2: Graphs, Equations of Lines, and Functions

Question 1

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

A)
B)
C)
D)
E)

Answer 1

Question 2

Determine which of the ordered pairs satisfy the given equation and then graph the equation by plotting the points that satisfy the equation.

A)
B)
C)
D)
E)

Answer 2

Question 3

Find the midpoint of segment PQ .

A)
B)
C)
D)
E)

Answer 3

Question 4

Graph the equation.

A)
B)
C)
D)
E)

Question 5

Graph the equation using the intercept method. Label the intercepts on the graph.

A)
B)
C)
D)
E)

Question 6

Find the slope of the line by finding the coordinates of two points on it. 10 x + 9 y = 9

A)
B)
C)
D)
E)

Question 7

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 8

Identify the correct location of the red dot on the rectangular coordinate system.

A) (-1, 3)
B) (4, -5)
C) (-4, 3)
D) (-3, 4)
E) None of these

Question 9

The equation 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 10

Find the midpoint of the segment PQ .

A)
B)
C)
D)
E)

Question 11

Graph the equation.

A)
B)
C)
D)
E)

Question 12

Find the coordinates of the point.

A) (3,-5)
B) (3,5)
C) (5,-3)
D) (1, 5)
E) (-5,-3)

Question 13

Graph the equation using the intercept method. Label the intercepts on the graph.

A)
B)
C)
D)
E)

Question 14

Find the midpoint of segment PQ .

A)
B)
C)
D)
E)

Question 15

Construct a table of solutions and graph of .

A)
B)
C)
D)

Question 16

Graph the equation using the intercept method. Label the intercepts on the graph.

A)
B)
C)
D)
E)

Question 17

Graph the linear equation.

A)
B)
C)
D)
E)

Question 18

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 19

Graph the equation.

A)
B)
C)
D)
E)

Question 20

Chase is studying the monthly percent changes in the stock price for two different companies. Using the data in the table below, plot the points for each month. Let the percent change for XM Inc. be the first number of the ordered pair, and let the percent change for Icom be the second number in the ordered pair.

A)
B)
C)
D)
E)

Question 21

Find the slope of the line determined by the equation.

A)
B)
C)
D)
E)

Question 22

Solve for y.

A)
B)
C)
D)

Question 23

Find the slope of the line determined by this pair of points. (3, -7), (4, -7) slope = __________

Question 24

Find the slope of the line determined by this pair of points. (5, 2), (10, 5)

A)
B)
C)
D)
E)

Question 25

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)
B) 45
C)
D) 14
E)

Question 26

Find the slope and the y -intercept of the line determined by the given equation.

A) slope: ; y -intercept:
B) slope: ; y -intercept:
C) slope: ; y -intercept:
D) slope: ; y -intercept:
E) slope: ; y -intercept:

Question 27

Use the point-slope form to write an equation of the line with the slope 7 and that passes through the point ( 9, 3). Then write your result in slope-intercept form.

A)
B)
C)
D)
E)

Question 28

Tell whether the slope of the line in the graph is positive , negative , zero , or undefined .

A) positive
B) zero
C) negative
D) undefined

Question 29

For the following pair of equations, predict whether they represent parallel lines, perpendicular lines, or lines that intersect but are not perpendicular. 2.1 x + 9.4 y = 3.9 and 9.4 x - 2.1 y = 8.6

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

Question 30

Determine the y -intercept of the line represented by the given equation.

A)
B)
C)
D)
E)

Question 31

Tell whether the slope of the line in the graph is positive , negative , zero , or undefined .

Question 32

The grade of a highway up a hill is 72%. How much change in horizontal distance is there if the vertical height of the hill is 200 feet? Express the answer to the nearest foot.

A) 297 ft
B) 278 ft
C) 178 ft
D) 288 ft
E) 253 ft

Question 33

If the ratio of rise to run is to be for some stairs and the measure of the run is 32 centimeters, find the measure of the rise to the nearest centimeter.

A) 64 cm
B) 15 cm
C) 16 cm
D) 26 cm
E) 31 cm

Question 34

Tell whether the lines with the given slopes are parallel, perpendicular, or neither.

A) perpendicular
B) parallel
C) neither

Question 35

Use the point-slope form to write an equation of the line with the slope 6 and that passes through the point (1, 9).

A) y + 1 = 6( x 9)
B) y 9 = 6( x + 1)
C) y + 9 = 6( x 1)
D) y 9 = 6( x 1)
E) y 1 = 6( x 9)

Question 36

Find the slope of the line determined by this pair of points.

A)
B)
C)
D)
E) undefined

Question 37

Determine the y -intercept of the line represented by the given equation.

A)
B)
C)
D)
E)

Question 38

Find the slope of the line determined by this pair of points. (3, -6), (7, -6) slope = __________

Question 39

Tell whether the graphs of the following pair of equations are parallel , perpendicular , or neither .

A) neither
B) parallel
C) perpendicular

Question 40

Use the point-slope form to write an equation of the line with the slope and that passes through the point .

A)
B)
C)
D)
E)

Question 41

For the following pair of equations, predict whether they represent parallel lines, perpendicular lines, or lines that intersect but are not perpendicular. 8.4 x + 8.1 y = 8.7 and 8.1 x - 8.4 y = 2.1

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

Question 42

Specify the range for the relation. {(3, 2), (5, 7), (13, 10), (16, 19)}

A) R = {3, 5, 13, 16}
B) R = {2, 19}
C) R = {2, 7, 10, 19}
D) R = {3, 5, 13, 16, 2, 7, 10, 19}
E) R = {3, 16}

Question 43

Graph the function and find its domain and range. f ( x ) = | x | - 2

A) D = (-∞, ∞), R = (-2, ∞)
B) D = (-∞, ∞), R = (-∞, ∞)
C) D = (-∞, ∞), R = (-∞, -2)
D) D = (-∞, ∞), R = (-∞, 2)

Question 44

Graph a linear equation using the slope and -intercept.

A)
B)
C)
D)

Question 45

Since 1990, when the average monthly price for basic cable TV programming in one country was $15.81, the cost has risen by about $1.62 a year. Write an equation in slope-intercept form to predict cable TV costs in the future. Use t to represent time in years after 1990 and C to represent the average basic monthly cost.

A)
B)
C)
D)
E)

Question 46

Graph the function and find its domain and range.

A) domain: ; range:
B) domain: ; range:
C) domain: ; range:
D) domain: ; range:

Question 47

The grade of a highway up a hill is 25%. How much change in horizontal distance is there if the vertical height of the hill is 150 feet? Express the answer to the nearest foot.

A) 619 ft
B) 600 ft
C) 500 ft
D) 610 ft
E) 575 ft

Question 48

Find an equation of the line that passes through the given point and is parallel to the given line. Write the equation in slope-intercept form.

A)
B)
C)
D)
E)

Question 49

Change the equation to slope-intercept form.

A)
B)
C)
D)
E)

Question 50

In the problem described below, assume that the relationship can be expressed as a linear equation in two variables, and use the given information to determine the equation. Express the equation in slope-intercept form. A new diet fad claims that a person weighing 150 pounds should consume 1,440 daily calories and that a 210-pound person should consume 1,600 calories. Let y represent the calories and x the weight of the person in pounds.

A)
B)
C)
D)
E)

Question 51

Specify the domain for the relation. {( x , y ) | 6 y - 7 x = 16}

A)
B)
C)
D)
E)

Question 52

Graph a linear equation using the slope and -intercept.

A)
B)
C)
D)

Question 53

Write the equation of the line that satisfies the given conditions. Express the final equation in standard form. contains the point (-1, 5) and is perpendicular to the line 6 x + 7 y = -6

A) 7 x - 6 y = -37
B) 7 x - 6 y = 23
C) 7 x + 6 y = -37
D) x - 6 y = 23
E) 7 x + 6 y = 23

Question 54

Tell whether the lines with the given slopes are parallel, perpendicular, or neither.

A) perpendicular
B) parallel
C) neither

Question 55

Tell whether the graphs of the following pair of equations are parallel , perpendicular , or neither .

A) neither
B) parallel
C) perpendicular

Question 56

Graph the function and find its domain and range. f ( x ) = -2| x | + 5

A) D = (-∞, ∞), R = (-5, ∞)
B) D = (-∞, ∞), R = (-∞, 5)
C) D = (-∞, ∞), R = (-∞, 5)
D) D = (-∞, ∞), R = (-∞, 5)

Question 57

Graph a linear equation using the slope and -intercept.

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

Question 58

Use the point-slope form to write an equation of the line with the slope 5 and that passes through the point ( 4, 7). Then write your result in slope-intercept form.

A)
B)
C)
D)
E)

Question 59

Write the equation of the line that satisfies the given conditions. Express the final equation in standard form. contains the point (5, 7) and is parallel to the line x -10 y = -5

A) x -10 y = -65
B) -10 x - y = -57
C) -10 x --11 y = -57
D) x -10 y = -5
E) -10 x - y = 65

Question 60

Specify the domain for the relation. { ( x , y ) | 5 x ² = 4 y ³ }

A)
B)
C)
D)
E)

Question 61

Tell whether the equation determines y to be a function of x .

A) no
B) yes

Question 62

Graph the linear equation.

A)
B)
C)
D)
E)

Question 63

If you have the following function, f ( x ) = - x ² - 6 x + 4, compute f (3), f (-1), f (7), f (-5).

A) f (3) = -3, f (-1) = 14, f (7) = 13, f (-5) = 62
B) f (3) = -5, f (-1) = 11, f (7) = 11, f (-5) = 59
C) f (3) = -2, f (-1) = 13, f (7) = 14, f (-5) = 61
D) f (3) = -4, f (-1) = 12, f (7) = 12, f (-5) = 60
E) f (3) = -6, f (-1) = 9, f (7) = 9, f (-5) = 58

Question 64

In the problem described below, assume that the relationship can be expressed as a linear equation in two variables, and use the given information to determine the equation. Express the equation in slope-intercept form. A new diet fad claims that a person weighing 170 pounds should consume 1,660 daily calories and that a 210-pound person should consume 1,800 calories. Let y represent the calories and x the weight of the person in pounds.

A)
B)
C)
D)
E)

Question 65

Determine the domain of the given function.

A)
B)
C)
D)

Question 66

Determine the domain of the given function.

A)
B)
C)
D)

Question 67

Graph the linear equation.

A)
B)
C)
D)
E)

Question 68

If you have the following function f ( x ) = 5 x + 6, compute f (5), f (-5), f (9), f (-9).

A) f (5) = 34, f (-5) = -21, f (9) = 54, f (-9) = -41
B) f (5) = 31, f (-5) = -19, f (9) = 51, f (-9) = -39
C) f (5) = 30, f (-5) = -18, f (9) = 50, f (-9) = -38
D) f (5) = 32, f (-5) = -20, f (9) = 52, f (-9) = -40
E) f (5) = -31, f (-5) = 19, f (9) = - 51, f (-9) = 39

Question 69

If you have the following function, f ( x ) = -9| x | + 5, compute f (4), f (-2), f (9), f (-7)

A) f (4) = -31, f (-2) = -13, f (9) = -76, f (-7) = -58
B) f (4) = -30, f (-2) = -14, f (9) = -75, f (-7) = -59
C) f (4) = -30, f (-2) = -11, f (9) = -77, f (-7) = -56
D) f (4) = -28, f (-2) = -15, f (9) = -73, f (-7) = -60
E) f (4) = 31, f (-2) = 13, f (9) = 76, f (-7) = 58

Question 70

Tell whether the equation determines y to be a function of x .

A) no
B) yes

Question 71

The graph represents a correspondence between x and y . Tell whether the correspondence is a function. If it is, give its domain and range.

A) a function with and .
B) a function with and .
C) a function with and .
D) a function with and .
E) not a function

Question 72

Graph the linear equation.

A)
B)
C)
D)
E)

Question 73

Tell whether the equation determines y to be a function of x . y = 8.5 x + 10

A) no
B) yes

Question 74

Graph the function. Check your work with a graphing calculator.

A)
B)
C)
D)

Question 75

Determine the domain of the given function.

A)
B)
C)
D)

Question 76

The graph of is the same as the graph of except that it is shifted __________.

A) 9 units down
B) 6 units to the right
C) 9 units up
D) 6 units up
E) 9 units to the left

Question 77

Since 1990, when the average monthly price for basic cable TV programming in one country was $15.41, the cost has risen by about $1.32 a year. Write an equation in slope-intercept form to predict cable TV costs in the future. Use t to represent time in years after 1990 and C to represent the average basic monthly cost.

A)
B)
C)
D)
E)

Question 78

Function of the graph.

A)
B)
C)
D)

Question 79

The boat swim y miles downstream in 5 hours. The speed of the boat in still water is 24 mph. Write the a linear equation that represent how distance depends from the speed of stream x .

A) y = 5 x + 120
B) y = 5 x + 24
C) y = 120 x + 5
D) y = 24 x + 120

Question 80

Graph the function.

A)
B)
C)
D)
E)