mac1147_lecture11_1_c

mac1147_lecture11_1_c - L11 Lines; Parallel and...

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105 L11 Lines; Parallel and Perpendicular Lines; Relations and Functions The Slope of a Line The slope m of a nonvertical line L is a ratio of the change in y , Rise , to the change in x , Run , that is: 21 yy Rise y m Run x x x == = , where ) , ( ), , ( 2 2 1 1 y x y x are any two distinct points on the line. The slope of a vertical line is undefined . Note : If 1 Run = , then Rise m = (slope). Example : Find the slope of the line whose graph is given below.
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106 Example : Find the slope of the line passing through the points (6 ,2 ) and ( 5, 4) −− (2 ,5) π and (7 , 5 ) (3, 2) and (3,5) Note : 1. A line with a positive slope rises from left to right. 2. A line with a negative slope falls from left to right. 3. A line with a zero slope is horizontal . 4. A line with undefined slope is vertical . Example: Draw the line that has slope 3 and passes through the point (1 ,4 ) .
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107 Equations of Lines A vertical line passing through the point ( , ) ab has an equation x a = , where a is also the x -intercept. Point-Slope Form of an Equation of a Line : A line with slope m passing through the point 11 (, ) x y has an equation () yy m xx =− .
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mac1147_lecture11_1_c - L11 Lines; Parallel and...

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