1. E QUATION OF A L INE Objective: Students will learn to derive the equation and y=mx by using similar triangles.

2. R ECAP : S LOPE For any line, the ratio of rise to run is constant (always the same). We call this ratio the slope of the line. 4 6 6 9

3. C OMMON M ISTAKE Be Careful!!!!! Slope can be use to find the equation of a given line. When that line passes through the origin (0,0). The general equation is where the m is the slope of the line.

4. H OW 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 Solve for y

5. H OW 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 general equation of a line.

6. R EMEMBER : Any point (x,y) on a line through the origin with slope m will satisfy is the equation of a line through the origin with slope=m.

7. T RY T HIS !!!! Use similar triangles to demonstrate that the equation of a line that passes through the origin with slope 2 is So Cross Multiply Create a triangle with slope

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