# 5. Build y = mx and y = mx + b equations from linear graphs using similar triangles (FP)

teaches Common Core State Standards CCSS.Math.Content.8.EE.B.6 http://corestandards.org/Math/Content/8/EE/B/6
teaches Common Core State Standards CCSS.Math.Practice.MP7 http://corestandards.org/Math/Practice/MP7

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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
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