Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line

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8.EE.B.6

**8.EE.B.6**: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

8.EE.B.6: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

What you'll learn

Construct slope triangles between two distinct points on a non-vertical line and explain how these triangles relate to the calculation of slope
Use the properties of similar triangles to prove that the slope between any two distinct points on a non-vertical line is always the same
Derive the equation y = mx for a line that passes through the origin, starting from the definition of slope and the similar triangles argument
Derive the equation y = mx + b for a line that intercepts the vertical axis at the point (0, b)
Connect the parameters m and b in the equation y = mx + b to their geometric meanings: m as the constant rate of change (slope) and b as the y-intercept

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Why slope is constant

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Deriving linear equations

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