The purpose of this lesson is for students to use the similarity relationship between slope triangles to write a relationship satisfied by any point on a non-vertical line. Students are shown a line on the coordinate plane that passes through and asked to determine if given points are on that line. Through repeated reasoning, students describe a rule that can test whether or not a point is on the line (MP8).

When students are shown a line that does not pass through , the key idea to introduce is that a point with coordinates represents a general point on the line. By noticing that all slope triangles lead to the same value of slope, this general point can be used to write a relationship satisfied by all points on the line (MP7).

In this example, the slope of the line is since the points and are on the line. The slope triangle in the picture has vertical length and horizontal length , giving the equation , which is satisfied by any point on the line, other than .