Lesson objective: Determine the equation of a linear function given two points by using similar triangles.

This lesson helps to build procedural skill with building linear equations of the form *y* = mx + b using similar triangles. Graphs are predominantly used here so that similar triangles can be utilized to help illustrate the equivalence of slope between all pairs of points on a given line. This work develops students' understanding that all "slope triangles" form segments from the same line are similar.

Students engage in Mathematical Practice 7 (Look for and make use of structure) as they work with the idea that the slope is equivalent between all pairs of points on a given line, and use this to find missing points and build equations.

**Key vocabulary:**

- equivalent ratio
- slope
- slope triangle
*y*-intercept