1140 L8 - ( x2 , y 2 ) ( x1 , y 1 ) ( x1 , y 1 )

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Lecture 8, part I: Section 1.3 Linear Equations in Two Variables Def. The equation Ax + By + C = 0 is the general form of a linear equation in two variables. The slope m of L is de±ned by the formula m = 2 2 1 1 ) ( ) ( x , y x , y Slope as a Rate of Change For line L , m is the quotient of the change in y , the Rise , and the change in x , the Run . We have m = Rise Run = ² y ² x = y 2 ± y 1 x 2 ± x 1 NOTE: The slope of a line measures the average rate of change of y with respect to x
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ex. Find the slope of the line through the points ( ± 6 ; 2) and ( ± 5 ; ± 4). NOTE: The order of subtraction is important!
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ex. Graph the equation x = 2. Equation of a Vertical Line A vertical line with x -intercept a is given by the equation ex. Graph the equation y = 3. Equation of a Horizontal Line A horizontal line with y -intercept b is given by the equation
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Now consider a nonvertical line L with slope m containing the point ( x 1 ; y 1 ) x , y ( ) 1 1 Let ( x; y ) be any other point on L. we have Point-Slope Form of the Equation of a Line A line L with slope m which passes through the point ( x 1 ; y 1 ) has equation ex. Write the equation of the line with slope 2 and containing ( ± 1 ; 1).
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ex. Write the equation of the line through (
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This note was uploaded on 07/08/2011 for the course MAC 1140 taught by Professor Williamson during the Spring '08 term at University of Florida.

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1140 L8 - ( x2 , y 2 ) ( x1 , y 1 ) ( x1 , y 1 )

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