Chapter 3 Linear Equations in Two Variables
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1 Chapter Linear Equations in Two Variables. Check Points. 6. x y x ( x, y) y ( ) 6, 6 y ( ), 0 y (0) 0, y () 0,0 y (),. E(, ) F(,0) G (6,0). a. xy 9 ( ) , true (, ) is a solution. b. xy 9 () , false (,) is not a solution... x y x ( x, y) y ( ), y ( ), 0 y (0) 0, y (), y () 8,8 x y x ( x, y) y ( ), y ( ), 0 y (0) 0 0,0 y (), y (), 7. x y x ( x, y) y ( ) 0,0 y ( ), 0 y (0) 0, y (), y (), 8. a. n D.n ( n, D) 0 D.(0) (0,) D.() 8 (,8) 0 D.(0) (0,) D.() (, ) Copyright 0 Pearson Education, Inc. 0
2 Chapter : Linear Equations in Two Variables b. Graph formula:. Quadrant IV 6. Quadrant III c. According to the graph, about 9% of consumers will pay primarily with debit cards in 0. d. D.n D.(0) 9 According to the formula, about 9% of consumers will pay primarily with debit cards in Quadrant II. Concept and Vocabulary Check. x-axis 0... y-axis. origin. quadrants; four. x-coordinate; y-coordinate 6. solution; satisfies 7. a/one 8. mx b. Exercise Set. Quadrant I 6. B (-,) 8. D (,-) 0. F (0,). H (.,0.). The x-coordinates are negative in Quadrants II and III. 6. The x- and y-coordinates have opposite signs in Quadrants II and IV. 0 Copyright 0 Pearson Education, Inc.
3 Introductory and Intermediate Algebra for College Students E Section y x, true, is a solution. y x 8, false, is not a solution. y x 0 0 0, true, 0 is a solution. y x, true, is a solution. y x , true 0,0 is a solution... y 8x , false 8,0 is not a solution. y 8x , false 6, is not a solution. y 8x 8 8, true, is a solution. xy , false, 0 is not a solution. y x 7, true 7, is a solution. xy , false 0,6 is not a solution. xy , false,0 is not a solution. Copyright 0 Pearson Education, Inc. 0
4 Chapter : Linear Equations in Two Variables 6. xy , true 0,0 is a solution. xy , false, is not a solution. xy , true, is a solution x y 0 x ( x, y) y 0 0, 0 y 0 0, 0 0 y ,0 y 0 0, 0 y 0 0, 0 x y 6x ( x, y) y 6 6, 6 y 6 0, 0 0 y 6 0 0, y 6, y 6 8,8 x y x9 ( x, y) y 9 9,9 y 9, 0 y ,9 y 9, y 9, 8. y 0 0 0, false 0, is not a solution. y , false,0 is not a solution. y , true 0, is a solution. 8. x y x ( x, y) y, y 0,0 0 y 0 0, y, y, 0. x y x ( x, y) y 8, 8 y, 0 y 0 0 0,0 y, y 8,8 0 Copyright 0 Pearson Education, Inc.
5 Introductory and Intermediate Algebra for College Students E Section. 60. x y x ( x, y) y, y, 0 y 0 0, y, y 0,0 66. x y x ( x, y) y, y, 0 y 0 0, y, y 8, 8 6. x y x ( x, y) y, y, 0 y 0 0, y, y, 68. x y x ( x, y) y, y, 0 y 00 0,0 y, y, 6. x y x ( x, y) y, y, 0 y 0 0, y, y, 70. x y x ( x, y) 8 y 8 8, y, 0 y 00 0,0 y, 8 y 8 8, Copyright 0 Pearson Education, Inc. 0
6 Chapter : Linear Equations in Two Variables 7. x y x ( x, y) 6 y 6 6, y, 0 y 0 0, y 0,0 6 y 6 6, 76. x y x ( x, y) y, y 6,6 0 y 0 0, y, y 9, 9 7. x y x ( x, y) y 8,8 y, 0 y 0 0, y, y, 78. x y x ( x, y) y.,. y.,. 0 y , 0. y.,. y.,. 06 Copyright 0 Pearson Education, Inc.
7 Introductory and Intermediate Algebra for College Students E Section. 80. y, or y 0x x y 0x ( x, y) 7 y 0 7 7, y 0, 0 y 0 0 0, y 0, 7 y 0 7 7, 9. a. n Q.7n ( n, Q) 0 Q.7(0) (0,) Q.7() 6. (,6.) 0 Q.7(0) 8 (0, 8) Q.7() 9. (,9.) 0 Q.7(0) (0,) b. Graph formula: 8. y x 8. y x c. According to the graph in part (b), the percentage is approximately %. d. Q.7n Q.7(8). According to the formula,.% of U.S. adults will believe that a college education is available to most qualified students in Answers will vary. 0. makes sense 86. a. xy.00 b. x.0.00 x x.00 x.00 An orange tree costs $ The coordinates of point B are (8,7). When the football is 8 yards from the quarterback, its height is 7 feet. 06. makes sense 08. true 0. false; Changes to make the statement true will vary. A sample change is: The point (,) satisfies the equation y x, but the point (, ) does not.. y x 90. The coordinates of point D are approximately (, 9.). 9. The football s height is feet when it is caught by the receiver. The receiver is 0 yards from the quarterback when he catches the ball. Two points on the graph are, and,. Copyright 0 Pearson Education, Inc. 07
8 Chapter : Linear Equations in Two Variables. y x. xy (0) y y y 6 The equation is satisfied by the ordered pair (0, 6). Two points on the graph are 6. Answers will vary. 7. x x 7 x8x7 x8x x8x 8x8x x x x 0 x 0 x. The solution set is V Ah for h V Ah V Ah V Ah V Ah A A V V h or h A A, and 6,. 0. xy x (0) x x 8 The equation is satisfied by the ordered pair (8,0).. xy 0 0y 0 y 0 y 0 The equation is satisfied by the ordered pair (0,0).. Check Points. a. The graph crosses the x-axis at (,0). Thus, the x-intercept is. The graph crosses the y-axis at (0,). Thus, the y-intercept is. b. The graph does not cross the x-axis. Thus, there is no x-intercept. The graph crosses the y-axis at (0,). Thus, the y-intercept is. c. The graph crosses the x-axis at (0,0). Thus, the x-intercept is 0. The graph crosses the y-axis at (0,0). Thus, the y-intercept is 0.. To find the x-intercept, let y = 0 and solve for x. xy x (0) x x The x-intercept is.. To find the y-intercept, let x = 0 and solve for y. xy (0) y y y The y-intercept is. 08 Copyright 0 Pearson Education, Inc.
9 Introductory and Intermediate Algebra for College Students E Section.. Find the x-intercept. Let y = 0 and solve for x. xy 6 x (0) 6 x 6 x The x-intercept is. Find the y- intercept. Let x = 0 and solve for y. xy 6 (0) y 6 y 6 y The y-intercept is. Find a checkpoint. For example, let x = and solve for y. xy 6 () y 6 y 6 y y or xy y y y 6. Because the constant on the right is 0, the graph passes through the origin. The x- and y-intercepts are both 0. Thus we will need to find two more points. Let y = and solve for x. xy 0 x ( ) 0 x 0 x Let y = and solve for x. xy 0 x () 0 x 0 x Use these three solutions of (0,0), (, ), and (,).. Find the x-intercept. Let y = 0 and solve for x. xy x (0) x The x-intercept is. Find the y- intercept. Let x = 0 and solve for y. xy 0y y y The y-intercept is. Find a checkpoint. For example, let x = and solve for y. 7. As demonstrated in the table below, all ordered pairs that are solutions of y have a value of y that is always. x y ( x, y), 0 0,, Thus the line is horizontal. Copyright 0 Pearson Education, Inc. 09
10 Chapter : Linear Equations in Two Variables 8. As demonstrated in the table below, all ordered pairs that are solutions of x have a value of x that is always. x y ( x, y), 0,0, Thus the line is vertical. 6. a. The graph crosses the x-axis at 0, 0 (the origin). Thus, the x-intercept is 0. b. The graph also crosses the y-axis at 0, 0. Thus, the y-intercept is a. The graph crosses the x-axis at, 0. Thus, the x-intercept is. b. The graph does not cross the y-axis. Thus, there is no y-intercept.. Concept and Vocabulary Check. x-intercept. y-intercept. x-intercept. y-intercept. standard 6. y; x 7. horizontal 8. vertical. Exercise Set. a. The graph crosses the x-axis at, 0. Thus, the x-intercept is. b. The graph crosses the y-axis at 0,. Thus, the y-intercept is.. a. The graph crosses the x-axis at, 0. Thus, the x-intercept is. 0. To find the x-intercept, let y = 0 and solve for x. x6y 0 x 600 x 0 x The x-intercept is. To find the y-intercept, let x = 0 and solve for y. x6y 0 06y 0 6y 0 y The y-intercept is.. To find the x-intercept, let y = 0 and solve for x. xy 0 x 00 x 0 0 x The x-intercept is. To find the y-intercept, let x = 0 and solve for y. xy 0 0y 0 y 0 y The y-intercept is. b. The graph crosses the y-axis at 0,. Thus, the y-intercept is. 0 Copyright 0 Pearson Education, Inc.
11 Introductory and Intermediate Algebra for College Students E Section.. To find the x-intercept, let y = 0 and solve for x. xy 0 x 0 0 x 0 x 0 The x-intercept is 0. To find the y-intercept, let x = 0 and solve for y. xy 0 0y 0 y 0 y 0 The y-intercept is To find the x-intercept, let y = 0 and solve for x. 8xy 0 8x 00 8x 0 x 0 The x-intercept is 0. To find the y-intercept, let x = 0 and solve for y. 8xy 0 80 y 0 y 0 y 0 The y-intercept is To find the x-intercept, let y = 0 and solve for x. x y x 0 x x The x-intercept is. 0. x y 6 x-intercept: 6 y-intercept: 6 checkpoint:, Draw a line through 6, 0, 0, 6, and. x y x-intercept: y-intercept: checkpoint:,,. Draw a line through,0,0,, and. 6xy x-intercept: y-intercept: 6 checkpoint:, Draw a line through,0,0, 6,,. and,. To find the y-intercept, let x = 0 and solve for y. x y 0 y y y The y-intercept is. Copyright 0 Pearson Education, Inc.
12 Chapter : Linear Equations in Two Variables 6. xy 0 x-intercept: 0 Draw a line through,0, 0,6, and,. y-intercept: 0 checkpoint:, Draw a line through 0 0, 0, 0,, and,. 8. x y x-intercept: y-intercept: checkpoint:,,0, 0,, Draw a line through and,.. x6y x-intercept: y-intercept: checkpoint:, Draw a line through, 0, 0,, and,. 0. x y 6 x-intercept: y-intercept: checkpoint:, Draw a line through, 00,, and,. 6. x y 0 x-intercept: 0 y-intercept: 0 The graph passes through the origin. Since the x and y intercepts are the same, two other points should be used. Second point:, Let x : y 0 y 0 y Let x : y 0 y 0 y checkpoint:, Draw a line through 0, 0,, and,.. 0y 60 0x x-intercept: y-intercept: 6 checkpoint:, Copyright 0 Pearson Education, Inc.
13 Introductory and Intermediate Algebra for College Students E Section. 8. yx 0 x-intercept: 0 y-intercept: 0 second point:, Let x : y 0 y 0 y checkpoint:, Draw a line through 0, 0,,, and,. 8. y All ordered pairs that are solutions will have a value of y that is. Any value can be used for x. Three ordered pairs that are solutions are,, 0,, and,. Plot these points and draw the line through them. The graph is a horizontal line. 0. xy 7 7 x-intercept: 7 y-intercept: checkpoint:, Draw a line through 7 7,0, 0,, and,. 0. y Three ordered pairs are,, 0,, and,. The graph is a horizontal line.. x All ordered pairs that are solutions will have a value of x that is. Any value can be used for y. Three ordered pairs that are solutions are,,, 0, and,. The graph is a vertical line.. The equation for this horizontal line is y. 7. The equation for this vertical line is x. (The equation can also be written as x. ). 6. The equation for this vertical line, which is the y- axis is x 0. Copyright 0 Pearson Education, Inc.
14 Chapter : Linear Equations in Two Variables. x 0 x Three ordered pairs are, and,. The graph is a vertical line.,, 0, 6. x 0 x x Three ordered pairs are,,, 0, and The graph is a vertical line.,. 6. y. 0 y. Three ordered pairs are,., 0,., and.,.. The graph is a horizontal line. 6. Using intercepts, we see that xy corresponds to Exercise. x-intercept: x 0 x y-intercept: 0y y y 66. Since x is a vertical line at, it corresponds to Exercise y 0 Three ordered pairs are, 0, 0, 0, and The graph is a horizontal line, the x-axis. 60. y 0 y, 0. Three ordered pairs are,, 0,, and The graph is a horizontal line.,. 68. Using intercepts, we see that xy 0 corresponds to Exercise. x-intercept: xy 0 x 0 0 x 0 x y-intercept: xy 0 0 y 0 y 0 y 70. a. The base of the trapezoid has length x and the top has length x y. The two sides each have length, so the perimeter equation for the x xy 8 trapezoid is given by: xxy08 xy x y 7 Copyright 0 Pearson Education, Inc.
15 Introductory and Intermediate Algebra for College Students E Section. b. The total perimeter is 8 feet and two sides are each feet. This leaves feet for the remaining two sides. Thus, the largest value possible for x is, which is when we have an isosceles triangle. 7. The eagle s height is increasing from 7 seconds to 0 seconds. 7. The equation is y. This means that the eagle s height remains constant at meters during the first three seconds of observation. 76. a. y 000x, x, x,000 x 8 After 8 years, the car is worth nothing. 90. does not make sense; Explanations will vary. Sample explanation: The graph of y. is a horizontal line. 9. Since the x-intercept is, y = 0 when x =.? x y? 0?? 6 So, the coefficient of x is 6. Similarly, since the y-intercept is, x = 0 when y =. 6 x? y 6(0)? ()? ()? So, the coefficient of y is. The equation of the line is 6xy. 9. x y y x b. y 000x,000 y 000(0),000 y,000 The new car is worth $,000. c. x and y must be non-negative because they represent time and the car s value. The y-intercept is. The x-intercept is. 96. xy 0 y x0 0 y x y x0 d. According to the graph, the car s value will be about $9000 after five years. Estimates will vary Answers will vary. 88. does not make sense; Explanations will vary. Sample explanation: The checkpoint must be a point other than the intercepts. The y-intercept is 0. The x-intercept is Copyright 0 Pearson Education, Inc.
16 Chapter : Linear Equations in Two Variables 7x x 7xx x ( x) ( x) 8x 8x6x68x 6x08x 6x8x08x8x x 00 x 0 x 0 x The solution set is,. y 0. y 0 x x 6 y 0. y ( ) x x 6 y 0. y 0 0 x x. Check Points. a. Let x y x y,, and,,. Change in y y y 6 m 6 Change in x x x ( ) The slope is 6. Since the slope is positive, the line rises from left to right. b. Let x y x y,, and,,. Change in y y y ( ) 7 7 m Change in x x x 7 The slope is. Since the slope is negative, the line falls from left to right.. a. Let x y x y, 6, and,,. Change in y y y 0 m 0 Change in x x x 6 Since the slope is 0, the line is horizontal. b. Let x y x y,,6 and,,. Change in y y y 6 m Change in x x x 0 Because division by 0 is undefined the slope is undefined. Since the slope is undefined, the line is vertical.. Line through (,) and (6,6): Change in y 6 m Change in x 6 Line through (0, ) and (,0): Change in y 0 ( ) m Change in x 0 Since their slopes are equal, the lines are parallel.. Line through (,) and (,): Change in y m Change in x ( ) Line through (, ) and (,7): Change in y 7 ( ) 8 m Change in x ( ) Since the product of their slopes is, the lines are perpendicular.. Let x, y990,9.0 and x, y 008,.7. Change in y y y m 0. Change in x x x The number of men living alone increased at a rate of 0. million per year. The rate of change is 0. million men per year.. Concept and Vocabulary Check. y x. y; x y x. positive. negative undefined 7. parallel 8. perpendicular 6 Copyright 0 Pearson Education, Inc.
17 Introductory and Intermediate Algebra for College Students E Section.. Exercise Set. Let x y x y,, and,,. Change in y y y m Change in x x x Since the slope is positive, the line rises from left to right.. Let x y x y,, and,,. Change in y y y m Change in x x x Since the slope is positive, the line rises from left to right. 6. Let x y x y y y y,, and,,. Change in 0 m 0 Change in x x x Since the slope is zero, the line is horizontal. 8. Let x y x y y y y, 6, and,,. Change in m Change in x x x 6 Since the slope is negative, the line falls from left to right. 0. Let x y x y y y y,, and,,. Change in 9 m ; Change in x x x 0 undefined Since the slope is undefined, the line is vertical.. Line through, and, : m. Line through, and, : m 6 6. Line through,, 0, and,0 : Use any two of these points to find the slope. m 0 8. Line through 0, and 6, 0 : 0 m Line through, and, : 0 m 0 (Since the line is horizontal, it is not necessary to do this computation. The slope of every horizontal line is 0).. Line through, and, m ; undefined 0 (Since this line is vertical, it is not necessary to do this computation. The slope of every vertical line is undefined.). Line through, and 6, : m 6 Line through, and, : m Since their slopes are equal the distinct lines are parallel. 6. Line through 7, 6 and 0, : 6 m Line through 9, and, : 8 m 9 0 Since their slopes are not equal, the distinct lines are not parallel. 8. Line through, and, : m Line through, and, : ( ) m Since the product of their slopes is, the lines are perpendicular. Copyright 0 Pearson Education, Inc. 7
18 Chapter : Linear Equations in Two Variables 0. Line through, 6 and, 6 : 6 ( 6) m ( ) Line through 8, and, : ( ) m ( 8) Since the product of their slopes is, the lines are not perpendicular.. Line through,7 and, : ( 7) m ( ) Line through, 9 and, : ( 9) m ( ) Since their slopes are equal the lines are parallel.. Line through, and 0, : ( ) m 6 0 ( ) Line through 0, 8 and, 6 : 6 ( 8) m 0 6 Since their slopes are not equal, nor are the slopes negative reciprocals, the lines are neither parallel nor perpendicular. 6. Line through, and 0, : 8. ( ) m 6 0 ( ) Line through, 6 and 6, : 6 m 6 ( ) 6 Since the product of their slopes is 6, 6 the lines are perpendicular. 0. y y 6 9 m x x y y m x x 9 y y 9 m x x 6 y y 6 m x x 6 9 Since m and m are the same, the line connecting, 6 and, is parallel to the line connecting, and 6,. Since m and m are the same, the line connecting, 6 and 6, is parallel to the line connecting,,. -0 y 0-0. First find the slope of the line passing through,,. and 0 x and 6 m Now, use the slope formula, the slope and the points (, y) and (7, ) to find y. y 7 y 6 8 y 6 y y 6 8 Copyright 0 Pearson Education, Inc.
19 Introductory and Intermediate Algebra for College Students E Section.. Find the slope of the line passing through, y 6. a. and,. y y y y m x x ( ) Find the slope of the line passing through, and,. y y ( ) m x x ( ) Since the lines are perpendicular, the product of their slopes is. y y 0 y 0 y 6 Change in y m 0. Change in x 6 0 b. For each year of aging, the percentage of Americans reporting a lot of stress decreases by 0.%. The rate of change is 0.% per year of aging. 66. Use the graph to observe where each line crosses the y-axis. In order of decreasing size, the y- intercepts are b, b, b, b. 68. y x 6 Two points on the graph are (0, 6) and (, ). 6 m y x 8. Change in y 6 feet 6 m Change in x 0 feet 0 The pitch of the roof is. 0. The grade of this ramp is foot % feet. 6. Answers will vary. 8. makes sense 60. does not make sense; Explanations will vary. Sample explanation: The slopes of the lines are both negative so they can not be perpendicular to each other. 6. true 6. false; Changes to make the statement true will vary. A sample change is: The slope of the line is undefined. Two points on the graph are (,) and (8,). 9 m 8 7. Let x = length of shorter piece (in inches). Let x = length of longer piece. xx 6 x 6 x The pieces are inches and inches Copyright 0 Pearson Education, Inc. 9
20 Chapter : Linear Equations in Two Variables 7. x x 8 x, 7. unit units right up (0, ) (,). y x The y-intercept is, so plot the point (0, ). The slope is m or m. Find another point by going up units and to the right unit. Use a straightedge to draw a line through the two points. 76. units units right down (0, ) (, ) 77. xy 0 xxy 0x y x x y y x. y x The y-intercept is, so plot the point (0,). The slope is m. Find another point by going up units and to the right units. Use a straightedge to draw a line through the two points.. Check Points. a. y x The slope is the x-coefficient, which is m. The y-intercept is the constant term, which is. b. y x The slope is the x-coefficient, which is m. The y-intercept is the constant term, which is. c. 7x y 6 y 7x 6 The slope is the x-coefficient, which is m 7. The y-intercept is the constant term, which is 6.. xy 0 y x y x The y-intercept is 0, so plot the point (0,0). The slope is m. Find another point by going down units and to the right units. Use a straightedge to draw a line through the two points. 0 Copyright 0 Pearson Education, Inc.
21 Introductory and Intermediate Algebra for College Students E Section.. a. The y-intercept is 8 and the slope is Change in y 8 6 m 0. Change in x The equation is y 0.x 8. b. y 0.x8 0.(60) 8 7. The model projects that 7.% of the U.S. population will be college graduates in 00.. Concept and Vocabulary Check. y mx b; slope; y-intercept. (0, ); ;. y. Exercise Set. y 9x The slope is the x-coefficient, which is 9. The y- intercept is the constant term, which is.. 6. y x y x m ; y-intercept = y x6 m ; y -intercept = 6 8. y 0x y 0x0 m 0; y-intercept = 0 0. y 7 y 0x7 m 0; y-intercept = 7. y x y xx m ; y-intercept =. 9x y 9x y9x 9x y 9x m 9; y-intercept = 6. x y 8 y x8x8 m ; y-intercept = x y 0 y 8x 8x0 m 8; y-intercept = 0 0. y 9x y x m ; y-intercept = 0. x9y 0 9y x y x 9 m ; y -intercept = 0 9. xy y x y x y x m ; y-intercept = 6. xy 0 y x0 y x 0 y x m ; y -intercept = Copyright 0 Pearson Education, Inc.
22 Chapter : Linear Equations in Two Variables 8. y x Step Plot 0, on the y-axis. Rise Step m Run Start at 0,. Using the slope, move units up (the rise) and unit to the right to reach the point,. Step Draw a line through 0, and,.. y x Slope = ; y-intercept = Plot 0,. From this point, move units up and units to the right to reach the point,. Draw a line through 0, and,. 0. y x Slope = ; y-intercept = Plot 0, on the y-axis. From this point, move units down (because is negative) and unit to the right to reach the point,. Draw a line through 0, and,. 6. y x m ; y-intercept = Plot 0,. From this pint, move units down and units to the right to reach the point,. Draw a line through 0, and,.. y x Slope = ;y-intercept = Plot 0,. From this point, move unit up and units to the right to reach the point,. Draw a line through 0, and,. 8. y x m ;y-intercept = 0 Plot 0, 0. From this point (the origin), move units down and units to the right to reach the point,. 0, 0 and,. Draw a line through Copyright 0 Pearson Education, Inc.
23 Introductory and Intermediate Algebra for College Students E Section. 0. a. x y 0 y x Draw a line through 0, and,. b. m ; y-intercept = 0 m, move units down and unit to the right to reach the point,. 0, 0 and,. c. Plot 0, 0. Since. a. y x y x b. Draw a line through m ; y-intercept = 0 c. Plot 0, 0. Move units up and units to the right to reach the point,. Draw a line through 0, 0 and,. 6. a. xy y x y x y x b. m ; y-intercept = 0,. Since m, move units down and units to the right to reach the point, 0. c. Plot Draw a line through 0, and, 0.. a. x y y x 8. y x: m ; y-intercept = y x m ; y-intercept = The lines are parallel because their slopes are equal. b. m ; y-intercept = m, move units down and unit to the right to reach the point,. c. Plot 0,. Since Copyright 0 Pearson Education, Inc.
24 Chapter : Linear Equations in Two Variables 0. y x m ; y-intercept = y x m ; y-intercept = The lines are not parallel because their slopes are not equal. The lines are not perpendicular because the product of their slopes is not. 6. x y y x xy 9 y x The lines are perpendicular because the product of their slopes is.. y x m ; y-intercept = y x m ; y-intercept = The lines are perpendicular because the product of their slopes is. 8. Find the slope of the parallel line. x y 8 y x8 The slope is. We are given that the y-intercept is, so using the slope-intercept form, we have y x. 60. The slope of the line y 8x is. The negative reciprocal of 8 is. 8 We are given that the y-intercept is 7, so using the slope-intercept form, we have y x xy 9 y x x9y 8 y x The lines are parallel because their slopes are equal. 6. Find the y-intercept of the line. y 6x8 y 6x 8 y x The y-intercept is. Now, find the slope of the parallel line. xy 0 y x0 y x 0 y x The slope is. Using the slope-intercept form, we have y x. Copyright 0 Pearson Education, Inc.
25 Introductory and Intermediate Algebra for College Students E Section. 6. If the line falls from left to right, the slope must be negative. It passes through the origin, 0, 0, and has a second point with opposite x- and y- coordinates. The point, is one example. Use the two points to find the slope. 0 m 0 The slope is. The y-intercept is 0. Using the slope-intercept form, we have y x0 or y x. 66. a. The y-intercept is and the slope is Change in y 0 m 0.6 Change in x 0 The equation is y 0.6x. b. y 0.6x 0.6(00) The model projects that % of the U.S. population will be Hispanic in Answers will vary. 70. makes sense 7. makes sense 7. false; Changes to make the statement true will vary. A sample change is: It is possible for m to equal b. 76. true 78. First, find the slope using the points 0, and 00, m The y-intercept is. Using slope-intercept form, 9 we have F C. x x Multiply by the LCD, which is. x x 7 x8x x 8 x x 8 The solution is {8} A =, P = % = 0. A PB 0.B 0.B B is % of y( x) yx y x7 8. y ( x) y x6 y x 8. y ( x0) y x.6 y 0.6x7. Copyright 0 Pearson Education, Inc.
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