chapter 1 - Chapter 1 Exercises 1.1 1. y = 2 5 x ;...

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Chapter 1 Exercises 1.1 25 x 1. ; y-intercept: 25 y =− ( ) 0,2 , slope = -5 2. 11 1 33 x y + == + 3 x ; y-intercept: 1 0, 3 ⎝⎠ , slope = 1 3 3. 21 3210 yx y x −− =⇒= + ; y-intercept: 1 0, 3 ⎛⎞ ⎜⎟ , slope = 2 3 4. ; y-intercept: , slope = 0 50 yy x =⇒ = + 5 ) ( 0,5 5. 31 1 x ; y-intercept: 1 0, 3 , slope = 1 6. 27 1 77 xy y x += −⇒= ; y-intercept: 1 0, 7 , slope = 2 7 7. slope = –7, (5, 0) on line. Let ( x , y ) = (5, 0), m = –7. y – 0 = –7( x – 5) y = –7 x + 35 8. slope = 0; (0, 0) on line. y -intercept (0, b ) = (0, 0), m = 0 y = mx + b y = 0 x + 0 y = 0 9. slope = 4; (1, 0) on line. Let ( x 1 , y 1 ) = (1,0), m = 4. y y 1 = m ( x x 1 ) y – 0 = 4( x – 1) y = 4 x – 4 10. slope = 7 3 ; (5, –1) on line. Let ( x 1 , y 1 ) = (5, 1), m = 7 3 . y y 1 = m ( x x 1 y ( 1) = 7 3 ( x 5) y + 1 = 7 3 x 35 3 y = 7 3 x 38 3 11. 2 3 ,5 and 5 6 , 4 on line. slope = y 2 y 1 x 2 x 1 = 4 5 5 6 2 3 = 9 9 6 = 6 Let ( x 1 , y 1 ) = 2 3 , m = 11 () 2 56 3 56 4 61 yy m xx −= −= − =+ 12. 1 2 ,1 and (1, 2) on line. slope = y 2 y 1 x 2 x 1 = 2 1 1 1 2 = 1 1 2 = 2 Let ( x 1 , y 1 ) = (1,2), m = 2. 22 ( 1 ) 2 = 13. (0, 0) and (1, –2) on line. slope = y 2 y 1 x 2 x 1 = 2 0 1 0 y – 0 = –2( x – 0) y = –2 x
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Chapter 1: The Derivative ISM: Calculus & Its Applications, 11e 26 14. 1 2 ,0 and (1, 2) on line. slope = y 2 y 1 x 2 x 1 = 2 0 1 −− 1 2 () = 2 3 2 = 4 3 = m Let ( x 1 , y 1 ) =− 1 2 . y y 1 = m ( x x 1 ) y 0 = 4 3 x 1 2 y = 4 3 x + 1 2 y = 4 3 x + 2 3 15. Horizontal through (3, –1). Let ( x 1 , y 1 ) = (3, 1), m = 0 (horizontal line). y y 1 = m ( x x 1 ) y ( 1) = 0( x 3) y + 1 = 0 y 1 16. x -intercept is 2; y -intercept is –2. The intercepts (2, 0) and (0, –2) are on the line. slope = y 2 y 1 x 2 x 1 = 2 0 0 2 = 1 = m y -intercept (0, b ) = (0, –2) y = mx + b y = 1 x – 2 y = x – 2 17. x -intercept is –1; y -intercept is 1. The intercepts (–1, 0) and (0, 1) are on the line. slope = y 2 y 1 x 2 x 1 = 1 0 0 ( = 1 y -intercept (0, b ) = (0, 1) y = mx + b y = 1 x + 1 y = x + 1 18. Slope = 6; x -intercept is –1. The x -intercept (–1, 0) is on the line. Let ( x 1 , y 1 ) = ( 1, 0), m = 6. y y 1 = m ( x x 1 ) y 0 = 6( x ( 1)) y = 6( x + 1) y = 6 x + 6 19. Slope = 1; x -intercept is –2. The x -intercept (–2, 0) is on the line. Let ( x 1 , y 1 ) = ( 2,0), m = 1. y y 1 = m ( x x 1 y – 0 = 1( x – (–2)) y = 1( x + 2) y = x + 2 20. Horizontal through (2 , 2 ) . Let 11 (, ) (2 ,2 ) , xy m = 0 (horizontal line). y y 1 = m ( x x 1 20 ( ( 2 ) ) 2 yx y = 21. Parallel to y = 2 x ; (2, 0) on line. slope = m = 2, ( x 1 , y 1 ) = (2,0) 02 ( 2 ) y = 2x - 4 yy m xx −= 22. Parallel to x + y = 0; (1, 1) on line. y = – x , slope = m = –1, ( x 1 , y 1 ) = (1,1) (1 ) y = -x + 2 −=− −=−+ 23. Parallel to 7 =−+ ; x-intercept is 1 7 , slope = m = –1, (, ) ( 1 , 0 ) = 011 1 =− + 24. Parallel to 13 = ; y-intercept is 1 2 13 = + , slope = m = 1, 1 0 , ) 2 1 1( 0) 2 1 2 1 2 +=
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ISM: Calculus & Its Applications, 11e Chapter 1: The Derivative 27 25. Perpendicular to y = 2 x ; (2, 0) on line.
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chapter 1 - Chapter 1 Exercises 1.1 1. y = 2 5 x ;...

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