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SLOPE INTERCEPT FORM Objective: In this lesson you will learn to derive the equation and y=mx+ b by using similar triangles. SLOPE-INTERCEPT FORM Slope can be use to find the equation of a given line. When that line crosses the y-axis not at the origin (0,0). The general equation is y mx b where the m is the slope of the line and b is the y-intercept. This is Slope-Intercept Form. SLOPE-INTERCEPT y mx b Slope y-intercept Y-INTERCEPT What is the y-intercept? The y-intercept is the point where the line crosses the y-axis. The vertical distance from the origin. This point is (0,y), x is always zero at this point. y-axis y-axis y-intercept x-axis x-axis y-intercept HOW DO WE FIND y mx b? Create a triangle with slope 2 3 Now we can make a triangle out of any coordinate (x,y), with slope y 2 x since we are no longer at the origin. y2 y2 2 So x 3 Cross Multiply 3 2 0 ,2 x 3 2 y2 x 0 ,0 3 y 2 2 x 3 y 6 2 x 2 Solve for y 3 y 2 x 6 y x 2 3 HOW DO WE FIND y mx? Create a triangle with slope m Now we can make a triangle out of any coordinate (x,y), with slope y b x 1 y b x x 1 m x 1 m 0,b 0 ,0 y b So y b m 1 Cross Multiply y b mx y mx b Thus we have the slope intercept form. REMEMBER: Any point (x,y) on a line across the yaxis with slope m will satisfy y mx b y mx b is the equation of a line that crosses the y-axis with slope=m. TRY THIS!! Create a triangle with slope -3 1 Now we can make a triangle out of any coordinate (x,y), with slope y 2 x 3 0 ,2 x x 1 3 y2 So y 2 3 x 1 Cross Multiply y2 1 0 ,0 y 2 -3 x y -3x 2 TRY THIS!!!! Use similar triangles to demonstrate that the equation of a line that passes through the point (0,-2) with slope 4 is y 4 x 2 Create a triangle with slope 4 1 1 1 y -2 4 4 x So y -2 4 Cross Multiply x 1 y 2 4x y 4x 2 0 ,0 0,-2 y -2 x