02_M_GOLD_9004_12_ch01-1 - Chapter 1 The Derivative 1.1 The...

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23 Chapter 1 The Derivative 1.1 The Slope of a Straight Line 1. 37 yx =− ; y -intercept: (0, 3), slope: ±7 2. 313 1 55 5 x + == + ; y -intercept: 1 0, 5 ⎛⎞ ⎜⎟ ⎝⎠ , slope: 3 5 3. 31 3 23 22 2 x xy y y x + = = + ; y -intercept: 3 0, 2 , slope: 1 2 4. 60 6 yy x =⇒= + ; y -intercept: (0, 6), slope: 0 5. 1 77 x x =−⇒= − ; y -intercept: (0, ±5), slope: 1 7 6. 41 4 1 49 1 99 9 x y y x −− += = = ; y -intercept: 1 0, 9 , slope = 4 9 7. slope = –1, (7, 1) on line. Let ( x , y ) = (7, 1), m = –1. ( ) 11 1(7 ) 8 −= − ⇒− = −−⇒ =− + yy m xx y x 8. slope = 2; (1, ±2) on line. Let ( x , y ) = (1, ±2), m = 2. ( ) ( 1 ) 24 −= − ⇒+= −⇒ y x 9. slope = 1 2 ; (2, 1) on line. ()() 1 Let , 2,1 ; . 2 m () 1 12 2 1 2 y x = −⇒ = 10. slope 7 ; 3 = , 45 on line. 7 Let , , ; . 3 m = 27 1 53 4 75 9 36 0 −= − ⇒+= − ⇒ y x 11. ,5 and , 4 ⎞⎛ ⎟⎜ ⎠⎝ on line. 21 1 0 7 9 6 3 slope 10 === = 56 3 Let , ,5 , . 71 0 m 63 5 5 10 7 y x −= − ⇒−= 12. 1 ,1 2 and (1, 4) on line. 41 3 slope= 6 1 = ( ) Let , (1,4), 6. m ( ) ( ) 46 1 62 y x −= − ⇒−= −⇒ 13. (0, 0) and (1, 0) on line. 00 slope 0 10 ( 0 ) 0 yxy = −= − ⇒= 14. , and 2 3 on line. ( ) 1 8 7 7 7 6 32 1 48 slope 49 m = = = 2 Let , ,1 . 3 = 48 2 1 49 3 48 17 49 49 y x = − ⇒ =+ 15. Horizontal through (2, 9). Let (, ) ( 2 , 9 ) , = m = 0 (horizontal line). ( ) ( ) 90 2 9 y x y =
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24 Chapter 1: The Derivative 16. x -intercept is 1; y -intercept is –3. The intercepts (1, 0) and (0, –3) are on the line. 21 30 slope 3 01 yy m xx −− == = = y -intercept (0, b ) = (0, –3) 33 ym xb y x =+ = 17. x -intercept is ; π y -intercept is 1. The intercepts ( ) ,0 and (0, 1) are on the line. 10 1 slope= 0( ) ππ y -intercept (0, b ) = (0, 1) 1 x xb y = + 18. Slope = 2; x -intercept is –3. The x -intercept (–3, 0) is on the line. Let 11 (, ) (3 , 0 ) , 2 . =− = xy m ( ) ( ) 02 3 26 yy m y x yx −= − ⇒−= +⇒ 19. Slope = ±2; x -intercept is –2. The x -intercept (–2, 0) is on the line. ( ) Let , ( 2,0), 2. m = ( ) ( ) 02 2 24 y x −= − ⇒−= − +⇒ 20. Horizontal through ( ) 7,2 . ( ) ( ) Let , 7, 2 , = m = 0 (horizontal line). () ( ) 20 7 2 y x y −= − ⇒−= − ⇒ = 21. Parallel to y = x ; (2, 0) on line. ( ) Let , (2,0); = slope = m = 1. ( ) ( ) 2 2 y x −= − ⇒−= −⇒ 22. Parallel to x + 2 y = 0; (1, 2) on line. ; 22 y x m += = = ( ) Let , (1, 2). = 1 2 15 y x − −⇒ + 23. Parallel to 37 ; x -intercept is 2. slope = m = 3. ( ) Let , (2, 0). = ( ) ( ) 03 2 36 y x 24. Parallel to 13 −= ; y -intercept is 0. 13 , slope = m = 1, b = 0. xb yx = 25. Perpendicular to y + x = 0; (2, 0) on line. 1 12 2 2 0 slope 1 1 1 Let ( , ) (2,0). y x m mm m m +=⇒= −⇒ = = ⋅= ⇒= = ( ) 2 2 yy mxx y x − = − ⇒−=−⇒ 26. Perpendicular to 51 ; + (1, 5) on line. slope = 1 5 m 2 2 1 1 5 m m =−⇒− =−⇒ = Let ( , ) (1,5). = 2 1 5 4 55 y x = 27. Start at (1, 0), then move one unit right and one unit up to (2, 1). 28. Start at (±1, 1), then move one unit up and two units to the right. 29. Start at (1, ±1), then move one unit up and three units to the left. Alternatively, move one unit down and three units to the right.
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Section 1.1 The Slope of a Straight Line 25 30. Start at (0, 2), then move zero units up and any distance (for example, one unit) right.
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This note was uploaded on 04/24/2010 for the course MATH 9374 taught by Professor Smith during the Spring '10 term at University of California, Berkeley.

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02_M_GOLD_9004_12_ch01-1 - Chapter 1 The Derivative 1.1 The...

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