1.4 - EXERCISES 1.4, page 41 1. e 7. 8. 2. c 3. a 4. d 5. f...

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EXERCISES 1.4, page 41 1. e 2. c 3. a 4. d 5. f 6. b 7. Referring to the figure shown in the text, we see that m = −− = 20 04 1 2 () . 8. Referring to the figure shown in the text, we see that m = =− 40 02 2. 9. This is a vertical line, and hence its slope is undefined. 10. This is a horizontal line, and hence its slope is 0. 11. m yy xx = = = 21 83 54 5. 12. m = = = 85 34 3 1 3 . 13. m = = = 42 5 6 14. m = = −−− = 2 6 1 3 15. m db ca = = . 16. m bb aa b a = = −− − +−−+ + ++ − = 1 11 1 12 2 . 17. Since the equation is in the slope-intercept form, we read off the slope m = 4. a. If x increases by 1 unit, then y increases by 4 units. b. If x decreases by 2 units, y decreases by 4(–2) = –8 units. 18. Rewrite the given equation in slope-intercept form: 234 34 2 4 3 2 3 xy y x y += = x = ,, . a. Since m = – 2/3, we conclude that the slope is negative. b. Since the slope is negative, y decreases as x increases in value. c. If x decreases by 2 units, then y increases by – (2/3)(–2) = 4/3 units. 19. The slope of the line through A and B is − − = = 10 2 31 8 4 2 . The slope of the line through C and D is 15 4 2 2 = = . Since the slopes of these two lines are equal, the lines are parallel. 1 Preliminaries 29
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20. The slope of the line through A and B is 23 22 . Since this slope is undefined, we see that the line is vertical.The slope of the line through C and D is 54 −−− () . Since this slope is undefined, we see that this line is also vertical. Furthermore, since the slopes of these two lines are equal, the lines are parallel. 21. The slope of the line through A and B is 25 42 3 6 1 2 −− =− . The slope of the line through C and D is 62 31 8 4 2 − − == . Since the slopes of these two lines are the negative reciprocals of each other, the lines are perpendicular. 22. The slope of the line through A and B is = = 20 12 2 1 2. The slope of the line through C and D is 84 2 12 1 6 = . Since the slopes of these two lines are not the negative reciprocals of each other, the lines are not perpendicular. 23. The slope of the line through the point (1, a ) and (4,– 2) is m a 1 2 41 = and the slope of the line through (2,8) and (–7, a + 4) is m a 2 48 72 = + . Since these two lines are parallel, m 1 is equal to m 2 . Therefore, 24 39 aa = 9( 2 ) 3( 4) 18 9 3 12 6 30 and 5 −−− = +=− = −= 24. The slope of the line through the point ( a , 1) and (5, 8) is m a 1 81 5 = , and the slope of the line through (4, 9) and ( a + 2,1) is m . a 2 19 = +− Since these two lines are parallel, m 1 is equal to m 2 . Therefore, 1 Preliminaries 30
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7 5 8 2 = aa , 7( a 2) = – 8(5 – a ), 7 a 14 = – 40 + 8 a, and a = 26. 25. An equation of a horizontal line is of the form y = b . In this case b = – 3, so y = – 3 is an equation of the line.
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1.4 - EXERCISES 1.4, page 41 1. e 7. 8. 2. c 3. a 4. d 5. f...

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