Question

Which shows how to use similar right triangles to find the equation of the line through (0,6) and any point (x,y), on the line?

Answer 1

By the given triangles in the figure, you can notice that the following proportion must be equal, because the involved sides are congruent:

`(y-b)/(x-0)=(m+b-b)/(1-0)`

In the left side, side of triangle with length y - b, divided by side with length x, must be equal to the quotient between side with length m + b - b and side with length 1.

Solve the previous equation for y, just as follow:

`\begin{gathered} (y-b)/(x)=m \\ y-b=mx \\ y=mx+b \end{gathered}`