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 where the m is the slope of the line and b is the y-intercept. This is Slope-Intercept Form.

Slope-Intercept y-intercept Slope

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.

How do we find So Solve for y Create a triangle with slope Now we can make a triangle out of any coordinate (x,y), with slope since we are no longer at the origin. So Cross Multiply Solve for y

Thus we have the slope intercept form. How do we find Create a triangle with slope Now we can make a triangle out of any coordinate (x,y), with slope So Cross Multiply Thus we have the slope intercept form.

Remember: Any point (x,y) on a line across the y-axis with slope m will satisfy is the equation of a line that crosses the y-axis with slope=m.

Try This!! Create a triangle with slope Now we can make a triangle out of any coordinate (x,y), with slope So Cross Multiply

Try This!!!! Use similar triangles to demonstrate that the equation of a line that passes through the point (0,-2) with slope 4 is Create a triangle with slope So Cross Multiply