By the given triangles in the figure, you can notice that the following proportion must be equal, because the involved sides are congruent:
[tex]\frac{y-b}{x-0}=\frac{m+b-b}{1-0}[/tex]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:
[tex]\begin{gathered} \frac{y-b}{x}=m \\ y-b=mx \\ y=mx+b \end{gathered}[/tex]