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Unformatted text preview: Lecture 8, part I: Section 1.3 Linear Equations in Two Variables Def. The equation u1D434u1D465 + u1D435u1D466 + u1D436 = 0 is the general form of a linear equation in two variables. The slope u1D45A of u1D43F is defined by the formula u1D45A = 2 2 1 1 ) ( ) ( x , y x , y Slope as a Rate of Change For line u1D43F , u1D45A is the quotient of the change in u1D466 , the Rise , and the change in u1D465 , the Run . We have u1D45A = Rise Run = Δ u1D466 Δ u1D465 = u1D466 2 − u1D466 1 u1D465 2 − u1D465 1 NOTE: The slope of a line measures the average rate of change of u1D466 with respect to u1D465 ex. Find the slope of the given line below: ex. Find the slope of the line through the points ( − 6 , 2) and ( − 5 , − 4). NOTE: The order of subtraction is important! ex. Graph the equation u1D465 = 2. Equation of a Vertical Line A vertical line with u1D465intercept u1D44E is given by the equation ex. Graph the equation u1D466 = 3. Equation of a Horizontal Line A horizontal line with u1D466intercept u1D44F is given by the equation Now consider a nonvertical line u1D43F with slope u1D45A containing the point ( u1D465 1 ,u1D466 1 ) x , y ( ) 1 1 Let ( u1D465,u1D466 ) be any other point on L. we have PointSlope Form of the Equation of a Line A line u1D43F with slope...
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This note was uploaded on 12/27/2011 for the course MAC 1147 taught by Professor German during the Summer '08 term at University of Florida.
 Summer '08
 GERMAN
 Calculus, Linear Equations, Equations, Rate Of Change, Slope

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