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

What you'll learn

1. Construct slope triangles between two distinct points on a non-vertical line and explain how these triangles relate to the calculation of slope
2. 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
3. Derive the equation y = mx for a line that passes through the origin, starting from the definition of slope and the similar triangles argument
4. Derive the equation y = mx + b for a line that intercepts the vertical axis at the point (0, b)
5. 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

Prerequisites

• Graph proportional relationships, interpreting the unit rate as the slope
• Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, and dilations