CWA CH 1 FINAL_97_10 - Chapter 1 LINEAR FUNCTIONS 8 4x 7y =...

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Chapter 1 LINEAR FUNCTIONS 1.1 Slopes and Equations of Lines 1. Find the slope of the line through (4 ; 5) and ( ¡ 1 ; 2) : m = 5 ¡ 2 4 ¡ ( ¡ 1) = 3 5 2. F indth es l op eo fth el in eth r ou gh (5 ; ¡ 4) and (1 ; 3) : m = 3 ¡ ( ¡ 4) 1 ¡ 5 = 3+4 ¡ 4 = ¡ 7 4 3. Find the slope of the line through (8 ; 4) and (8 ; ¡ 7) : m = 4 ¡ ( ¡ 7) 8 ¡ 8 = 11 0 The slope is unde…ned; the line is vertical. 4. Find the slope of the line through (1 ; 5) and ( ¡ 2 ; 5) : m = 5 ¡ 5 ¡ 2 ¡ 1 = 0 ¡ 3 =0 5. y = x Using the slope-intercept form, y = mx + b ,w e see that the slope is 1. 6. y =3 x ¡ 2 This equation is in slope-intercept form, y = mx + b . Thus, the coe¢cient of the x -term, 3, is the slope. 7. 5 x ¡ 9 y =11 Rewrite the equation in slope-intercept form. 9 y =5 x ¡ 11 y = 5 9 x ¡ 11 9 The slope is 5 9 : 8. 4 x +7 y =1 Rewrite the equation in slope-intercept form. 7 y =1 ¡ 4 x 1 7 (7 y )= 1 7 (1) ¡ 1 7 (4 x ) y = 1 7 ¡ 4 7 x y = ¡ 4 7 x + 1 7 The slope is ¡ 4 7 : 9. x =5 This is a vertical line. The slope is unde…ned. 10. The x -axis is the horizontal line y =0 : Horizontal lines have a slope of 0. 11. y =8 This is a horizontal line, which has a slope of 0. 12. y = ¡ 6 By rewriting this equation in the slope-intercept form, y = mx + b; we get y =0 x ¡ 6 ; with the slope, m; being 0. 13. Find the slope of a line parallel to 6 x ¡ 3 y =12 : Rewrite the equation in slope-intercept form. ¡ 3 y
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Section 1.1 Slopes and Equations of Lines 57 14. Find the slope of a line perpendicular to 8 x =2 y ¡ 5 : First, rewrite the given equation in slope-intercept form. 8 x =2 y ¡ 5 8 x +5=2 y 4 x + 5 2 = y or y =4 x + 5 2 Let m be the slope of any line perpendicular to the given line. Then 4 ¢ m = ¡ 1 m = ¡ 1 4 : 15. The line goes through (1 ; 3) ; with slope m = ¡ 2 : Use point-slope form. y ¡ 3= ¡ 2( x ¡ 1) y = ¡ 2 x +2+3 y = ¡ 2 x +5 16. The line goes through (2 ; 4) ; with slope m = ¡ 1 : Use point-slope form. y ¡ 4= ¡ 1( x ¡ 2) y ¡ 4= ¡ x +2 y = ¡ x +6 17. The line goes through ( ¡ 5 ; ¡ 7) with slope m =0 . Use point-slope form. y ¡ ( ¡ 7) = 0[ x ¡ ( ¡ 5)] y +7=0 y = ¡ 7 18. The line goes through ( ¡ 8 ; 1) ; with unde…ned slope. Since the slope is unde…ned, the line is vertical. The equation of the vertical line passing through ( ¡ 8 ; 1) is x = ¡ 8 : 19. Thel inegoesthrough (4 ; 2) and (1 ; 3) : Find the slope, then use point-slope form with either of the two given points. m = 3 ¡ 2 1 ¡ 4 = ¡ 1 3 y ¡ 3= ¡ 1 3 ( x ¡ 1) y = ¡ 1 3 x + 1 3 +3 y = ¡ 1 3 x + 10 3 20. Thel inegoesthrough (8 ; ¡ 1) and (4 ; 3) : Find the slope, then use point-slope form with
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This note was uploaded on 10/07/2010 for the course CALC 2302 taught by Professor Yuly during the Fall '08 term at University of Texas at Dallas, Richardson.

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CWA CH 1 FINAL_97_10 - Chapter 1 LINEAR FUNCTIONS 8 4x 7y =...

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