Here is a line on the coordinate plane.

Coordinate plane, x, negative 1 to 6, y negative 1 to 8. A line through point A, at 0 comma 1, point C at 1 comma 3, and point E at x comma y. A dotted line connects C to B at 1 comma 1. Another connects E to D at x comma 1. The length of E D is y minus 1. The length of A,  D is x.  

The points , , and are on the same line. Triangles and are slope triangles for the line, so they are similar triangles. We can use their similarity to better understand the relationship between and , which are the coordinates of point .

• The slope for triangle is because the vertical side has length 2 and the horizontal side has length 1.
• For triangle , the vertical side has length  because  is the distance from point to the -axis, and side  is 1 unit shorter than the distance. The horizontal side has length . So, the slope for triangle is .
• The slopes for the two slope triangles are equal, meaning .

The equation is true for all points on the line.