1. Slope -intercept form
Objective: In this lesson you will learn to derive the equation and y=mx+ b by using similar triangles.

2. 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.

3. Slope-Intercept
y-intercept
Slope

4. 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.

5. 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

6. 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.

7. 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.

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

9. 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