mac1147_lecture9_1_b

mac1147_lecture9_1_b - L9 Lines; Parallel and Perpendicular...

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101 L9 Lines; Parallel and Perpendicular Lines; Relations and Functions; Operations on 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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102 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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103 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 =− . A horizontal line passing through the point ( , ) has an equation yb = , where b is also the y -intercept.
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104 Example . Find an equation of the line passing through (3 ,5 ) with slope 2 m = − .
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mac1147_lecture9_1_b - L9 Lines; Parallel and Perpendicular...

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