Chapter 4 Review Exercises
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Chapter 4 Review Exercises
Rectangular Coordinate System
Plot Points in a Rectangular Coordinate System
In the following exercises, plot each point in a rectangular coordinate system.
Exercise 1
- (−1,−5)
- (−3,4)
- (2,−3)
- (1,52)
Exercise 2
- (4,3)
- (−4,3)
- (−4,−3)
- (4,−3)
- Answer
-
Exercise 3
- (−2,0)
- (0,−4)
- (0,5)
- (3,0)
Exercise 4
- (2,32)
- (3,43)
- (13,−4)
- (12,−5)
- Answer
-
Identify Points on a Graph
In the following exercises, name the ordered pair of each point shown in the rectangular coordinate system.
Exercise 5
Exercise 6
- Answer
-
a. (2,0)
b (0,−5)
c (−4.0)
d (0,3)
Verify Solutions to an Equation in Two Variables
In the following exercises, which ordered pairs are solutions to the given equations?
Exercise 7
5x+y=10
- (5,1)
- (2,0)
- (4,−10)
Exercise 8
y=6x−2
- (1,4)
- (13,0)
- (6,−2)
- Answer
-
1, 2
Complete a Table of Solutions to a Linear Equation in Two Variables
In the following exercises, complete the table to find solutions to each linear equation.
Exercise 9
y=4x−1
x | y | (x,y) |
0 | ||
1 | ||
-2 |
Exercise 10
y=−12x+3
x | y | (x,y) |
0 | ||
4 | ||
-2 |
- Answer
-
x y (x,y) 0 3 (0,3) 4 1 (4, 1) −2 4 (−2,4)
Exercise 11
x+2y=5
x | y | (x,y) |
0 | ||
1 | ||
-1 |
Exercise 12
3x+2y=6
x | y | (x,y) |
0 | ||
0 | ||
-2 |
- Answer
-
x y (x,y) 0 −3 (0,−3) 2 0 (2,0) −2 −6 (−2,−6)
Find Solutions to a Linear Equation in Two Variables
In the following exercises, find three solutions to each linear equation.
Exercise 13
x+y=3
Exercise 14
x+y=−4
- Answer
-
Answers will vary.
Exercise 15
y=3x+1
Exercise 16
y=−x−1
- Answer
-
Answers will vary.
Graphing Linear Equations
Recognize the Relation Between the Solutions of an Equation and its Graph
In the following exercises, for each ordered pair, decide:
- Is the ordered pair a solution to the equation?
- Is the point on the line?
Exercise 17
y=−x+4
(0,4) (−1,3)
(2,2) (−2,6)
Exercise 18
y=23x−1
(0,−1)(3,1)
(−3,−3)(6,4)
- Answer
-
- yes; yes
- yes; no
Graph a Linear Equation by Plotting Points
In the following exercises, graph by plotting points.
Exercise 19
y=4x−3
Exercise 20
y=−3x
- Answer
-
Exercise 21
y=12x+3
Exercise 22
x−y=6
- Answer
-
Exercise 23
2x+y=7
Exercise 24
3x−2y=6
- Answer
-
Graph Vertical and Horizontal lines
In the following exercises, graph each equation.
Exercise 25
y=−2
Exercise 26
x=3
- Answer
-
In the following exercises, graph each pair of equations in the same rectangular coordinate system.
Exercise 27
y=−2x and y=−2
Exercise 28
y=43x and y=43
- Answer
-
Graphing with Intercepts
Identify the x- and y-Intercepts on a Graph
In the following exercises, find the x- and y-intercepts.
Exercise 29
Exercise 30
- Answer
-
(3,0) and (0,3)
Find thex- and y-Intercepts from an Equation of a Line
In the following exercises, find the intercepts of each equation.
Exercise 31
x+y=5
Exercise 32
x−y=−1
- Answer
-
(−1,0),(0,1)
Exercise 33
x+2y=6
Exercise 34
2x+3y=12
- Answer
-
(6,0),(0,4)
Exercise 35
y=34x−12
Exercise 36
y=3x
- Answer
-
(0,0)
Graph a Line Using the Intercepts
In the following exercises, graph using the intercepts.
Exercise 37
−x+3y=3
Exercise 38
x+y=−2
- Answer
-
Exercise 39
x−y=4
Exercise 40
2x−y=5
- Answer
-
Exercise 41
2x−4y=8
Exercise 42
y=2x
- Answer
-
Slope of a Line
Use Geoboards to Model Slope
In the following exercises, find the slope modeled on each geoboard.
Exercise 43
Exercise 44
- Answer
-
43
Exercise 45
Exercise 46
- Answer
-
−23
Exercise 47
13
Exercise 48
32
- Answer
-
Exercise 49
−23
Exercise 50
−12
- Answer
-
Use m= rise run to find the Slope of a Line from its Graph
In the following exercises, find the slope of each line shown.
Exercise 51
Exercise 52
- Answer
-
1
Exercise 53
Exercise 54
- Answer
-
−12
Find the Slope of Horizontal and Vertical Lines
In the following exercises, find the slope of each line.
Exercise 55
y=2
Exercise 56
x=5
- Answer
-
undefined
Exercise 57
x=−3
Exercise 58
y=−1
- Answer
-
0
Use the Slope Formula to find the Slope of a Line between Two Points
In the following exercises, use the slope formula to find the slope of the line between each pair of points.
Exercise 59
(−1,−1),(0,5)
Exercise 60
(3,5),(4,−1)
- Answer
-
−6
Exercise 61
(−5,−2),(3,2)
Exercise 62
(2,1),(4,6)
- Answer
-
52
Graph a Line Given a Point and the Slope
In the following exercises, graph each line with the given point and slope.
Exercise 63
(2,−2);m=52
Exercise 64
(−3,4);m=−13
- Answer
-
Exercise 65
x -intercept −4;m=3
Exercise 66
y -intercept 1;m=−34
- Answer
-
Solve Slope Applications
In the following exercises, solve these slope applications.
Exercise 67
The roof pictured below has a rise of 10 feet and a run of 15 feet. What is its slope?
Exercise 68
A mountain road rises 50 feet for a 500-foot run. What is its slope?
- Answer
-
110
Intercept Form of an Equation of a Line
Recognize the Relation Between the Graph and the Slope–Intercept Form of an Equation of a Line
In the following exercises, use the graph to find the slope and y-intercept of each line. Compare the values to the equation y=mx+b.
Exercise 69
y=4x−1
Exercise 70
y=−23x+4
- Answer
-
slope m=−23 and y-intercept (0,4)
Identify the Slope and y-Intercept from an Equation of a Line
In the following exercises, identify the slope and y-intercept of each line.
Exercise 71
y=−4x+9
Exercise 72
y=53x−6
- Answer
-
53;(0,−6)
Exercise 73
5x+y=10
Exercise 74
4x−5y=8
- Answer
-
45;(0,−85)
Graph a Line Using Its Slope and Intercept
In the following exercises, graph the line of each equation using its slope and y-intercept.
Exercise 75
y=2x+3
Exercise 76
y=−x−1
- Answer
-
Exercise 77
y=−25x+3
Exercise 78
4x−3y=12
- Answer
-
In the following exercises, determine the most convenient method to graph each line.
Exercise 79
x=5
Exercise 80
y=−3
- Answer
-
horizontal line
Exercise 81
2x+y=5
Exercise 82
x−y=2
- Answer
-
intercepts
Exercise 83
y=x+2
Exercise 84
y=34x−1
- Answer
-
plotting points
Graph and Interpret Applications of Slope–Intercept
Exercise 85
Katherine is a private chef. The equation C=6.5m+42 models the relation between her weekly cost, C, in dollars and the number of meals, m, that she serves.
- Find Katherine’s cost for a week when she serves no meals.
- Find the cost for a week when she serves 14 meals.
- Interpret the slope and C-intercept of the equation.
- Graph the equation.
Exercise 86
Marjorie teaches piano. The equation P=35h−250 models the relation between her weekly profit, P, in dollars and the number of student lessons, s, that she teaches.
- Find Marjorie’s profit for a week when she teaches no student lessons.
- Find the profit for a week when she teaches 20 student lessons.
- Interpret the slope and P-intercept of the equation.
- Graph the equation.
- Answer
-
- −$250
- $450
- The slope, 35, means that Marjorie’s weekly profit, P, increases by $35 for each additional student lesson she teaches. The P-intercept means that when the number of lessons is 0, Marjorie loses $250.
Use Slopes to Identify Parallel Lines
In the following exercises, use slopes and y-intercepts to determine if the lines are parallel.
Exercise 87
4x−3y=−1;y=43x−3
Exercise 88
2x−y=8;x−2y=4
- Answer
-
not parallel
Use Slopes to Identify Perpendicular Lines
In the following exercises, use slopes and y-intercepts to determine if the lines are perpendicular.
Exercise 89
y=5x−1;10x+2y=0
Exercise 90
3x−2y=5;2x+3y=6
- Answer
-
perpendicular
Find the Equation of a Line
Find an Equation of the Line Given the Slope and y-Intercept
In the following exercises, find the equation of a line with given slope and y-intercept. Write the equation in slope–intercept form.
Exercise 91
slope 13 and y-intercept (0,−6)
Exercise 92
slope −5 and y-intercept (0,−3)
- Answer
-
y=−5x−3
Exercise 93
slope 0 and y-intercept (0,4)
Exercise 94
slope −2 and y-intercept (0,0)
- Answer
-
y=−2x
In the following exercises, find the equation of the line shown in each graph. Write the equation in slope–intercept form.
Exercise 95
Exercise 96
- Answer
-
y=−3x+5
Exercise 97
Exercise 98
- Answer
-
y=−4
Find an Equation of the Line Given the Slope and a Point
In the following exercises, find the equation of a line with given slope and containing the given point. Write the equation in slope–intercept form.
Exercise 99
m=−14, point (−8,3)
Exercise 100
m=35, point (10,6)
- Answer
-
y=35x
Exercise 101
Horizontal line containing (−2,7)
Exercise 102
m=−2, point (−1,−3)
- Answer
-
y=−2x−5
Find an Equation of the Line Given Two Points
In the following exercises, find the equation of a line containing the given points. Write the equation in slope–intercept form.
Exercise 103
(2,10) and (−2,−2)
Exercise 104
(7,1) and (5,0)
- Answer
-
y=12x−52
Exercise 105
(3,8) and (3,−4)
Exercise 106
(5,2) and (−1,2)
- Answer
-
y=2
Find an Equation of a Line Parallel to a Given Line
In the following exercises, find an equation of a line parallel to the given line and contains the given point. Write the equation in slope–intercept form.
Exercise 107
line y=−3x+6, point (1,−5)
Exercise 108
line 2x+5y=−10, point (10,4)
- Answer
-
y=−25x+8
Exercise 109
line x=4, point (−2,−1)
Exercise 110
line y=−5, point (−4,3)
- Answer
-
y=3
Find an Equation of a Line Perpendicular to a Given Line
In the following exercises, find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope–intercept form.
Exercise 111
line y=−45x+2, point (8,9)
Exercise 112
line 2x−3y=9, point (−4,0)
- Answer
-
y=−32x−6
Exercise 113
line y=3, point (−1,−3)
Exercise 114
line x=−5 point (2,1)
- Answer
-
y=1
Graph Linear Inequalities
Verify Solutions to an Inequality in Two Variables
In the following exercises, determine whether each ordered pair is a solution to the given inequality.
Exercise 115
Determine whether each ordered pair is a solution to the inequality y<x−3:
- (0,1)
- (−2,−4)
- (5,2)
- (3,−1)
- (−1,−5)
Exercise 116
Determine whether each ordered pair is a solution to the inequality x+y>4:
- (6,1)
- (−3,6)
- (3,2)
- (−5,10)
- (0,0)
- Answer
-
- yes
- no
- yes
- yes
- no
Recognize the Relation Between the Solutions of an Inequality and its Graph
In the following exercises, write the inequality shown by the shaded region.
Exercise 117
Write the inequality shown by the graph with the boundary line y=−x+2.
Exercise 118
Write the inequality shown by the graph with the boundary line y=23x−3
- Answer
-
y>23x−3
Exercise 119
Write the inequality shown by the shaded region in the graph with the boundary line x+y=−4.
Exercise 120
Write the inequality shown by the shaded region in the graph with the boundary line x−2y=6.
- Answer
-
x−2y≥6
Graph Linear Inequalities
In the following exercises, graph each linear inequality.
Exercise 121
Graph the linear inequality y>25x−4
Exercise 122
Graph the linear inequality y≤−14x+3
- Answer
-
Exercise 123
Graph the linear inequality x−y≤5
Exercise 124
Graph the linear inequality 3x+2y>10
- Answer
-
Exercise 125
Graph the linear inequality y≤−3x
Exercise 126
Graph the linear inequality y<6
- Answer
-
Practice Test
Exercise 1
Plot each point in a rectangular coordinate system.
- (2,5)
- (−1,−3)
- (0,2)
- (−4,32)
- (5,0)
Exercise 2
Which of the given ordered pairs are solutions to the equation 3x−y=6?
- (3,3)
- (2,0)
- (4,−6)
- Answer
-
- yes
- yes
- no
Exercise 3
Find three solutions to the linear equation y=−2x−4
Exercise 4
Find the x- and y-intercepts of the equation 4x−3y=12
- Answer
-
(3,0),(0,−4)
Find the slope of each line shown.
Exercise 5
Exercise 6
- Answer
-
undefined
Exercise 7
Exercise 8
Find the slope of the line between the points (5,2) and (−1,−4)
- Answer
-
1
Exercise 9
Graph the line with slope 12 containing the point (−3,−4)
Graph the line for each of the following equations.
Exercise 10
y=53x−1
- Answer
-
Exercise 11
y=−x
Exercise 12
x−y=2
- Answer
-
Exercise 13
4x+2y=−8
Exercise 14
y=2
- Answer
-
Exercise 15
x=−3
Find the equation of each line. Write the equation in slope–intercept form.
Exercise 16
slope −34 and y-intercept (0,−2)
- Answer
-
y=−34x−2
Exercise 17
m=2, point (−3,−1)
Exercise 18
containing (10,1) and (6,−1)
- Answer
-
y=12x−4
Exercise 19
parallel to the line y=−23x−1, containing the point (−3,8)
Exercise 20
perpendicular to the line y=54x+2, containing the point (−10,3)
- Answer
-
y=−45x−5
Exercise 21
Write the inequality shown by the graph with the boundary line y=−x−3.
Graph each linear inequality.
Exercise 22
y>32x+5
- Answer
-
Exercise 23
x−y≥−4
Exercise 24
y≤−5x
- Answer
-
Exercise 1
y<3