"Graphing Linear Equations and Using Slope Slopes and Intercepts"
Graphing Linear Equations and Using Slope Lessons 12-1,12-2 Why? Many relationships can be represented by linear equations. The slope of a linear graph is a measure of the rate of change of one variable with respect to the other variable. Graph linear equation y 2x 1. y x y 4 (2, 5) Positive Negative 1 1 y2 y1 slope slope rise 0 1 Slope 2 run x2 x1 2 5 (0, 1) x 4 2 O 2 4 ( 1, 1) 2 Zero Undefined slope slope 4 Slopes and Intercepts Lesson 12-3 Why? The slope-intercept form of an equation of a line is often used to express a relationship. Intercepts of a Line Slope-Intercept Form of Standard Form of a y a Linear Equation Linear Equation 4 y-intercept = 2 Slope y-intercept Ax By C, (0, 2) x-intercept = 3 where A, B, and C 2 (3, 0) x y mx b are real numbers. 2 O 2 4 To graph a linear equation in To graph a linear equation in 2 this form, plot the y-intercept, this form, ﬁnd the x-intercept b, at (0, b). Then use the slope and the y-intercept. Then plot to ﬁnd a second point. and connect the two points. Point-Slope Form Lesson 12-4 Why? The point-slope form of a linear equation is convenient for some purposes. Point-Slope Form of a Write an equation of the line with 1 Linear Equation slope 2 that passes through point ( 3, 5). y y1 m(x x1) y y1 m(x x1) (x1, y1) is a point on the 1 y 5 2 (x ( 3)) line. m is the 1 y 5 2 (x 3) slope of the line. 628B