How do similar triangles show that slope is constant?

Similar triangles have proportional sides, so rise over run is the same for a small triangle and a large one on the same line. That shared ratio is the slope m. Students check this by counting both triangles on four lines.

How do you derive y = mx + b from similar triangles?

For a line through (0, b), a triangle from (0, b) to any point (x, y) has rise y minus b and run x. Setting that ratio equal to m and multiplying by x, then adding b, gives y = mx + b. Use Similar Triangles to Derive y = mx + b guides this in parts.

8th Grade Similar Triangles and Slope Worksheets

Ages 13-14 · Free previews · Print-ready PDFs

Written by Adi Ackerman, Head Teacher

Slope triangles drawn on the same line are similar, so their rise over run is always equal, and that equal ratio is the slope. There are 2 sheets for 8th grade here, each with an answer key. Slope Triangles on One Line Are Similar has students count rise and run on a small and a large triangle along four lines. Use Similar Triangles to Derive y = mx + b walks through the argument for a line through the origin and a line through (0, b). Both sheets practice 8.EE.B.6.

8th Grade Math Linear Equations Similar triangles and slope Clear All

$Slope Triangles on One Line Are Similar - 8th Grade Linear Equations worksheet preview$

Slope Triangles on One Line Are Similar

Grade8th Grade

TopicLinear Equations

$Use Similar Triangles to Derive y = mx + b - 8th Grade Linear Equations worksheet preview$

Use Similar Triangles to Derive y = mx + b

Grade8th Grade

TopicLinear Equations

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Frequently Asked Questions

Each slope triangle has a right angle, and the line meets each triangle's run at the same angle because they lie on one line. Triangles with two equal angles are similar. Slope Triangles on One Line Are Similar asks students to explain this in one sentence.

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