Question

the red and the blue triangles drawn on the line are similar. what equation can be used to show that the slope of the line is the same between any two points? rise 1·run 1 = rise 2·run 2 \\(\frac{rise\\ 1}{run\\ 1} = \frac{rise\\ 2}{run\\ 2}\\) rise 1+run 1 = rise 2+run 2 \\(\frac{run\\ 1}{rise\\ 2} = \frac{run\\ 2}{rise\\ 1}\\)

Explanation:

Step1: Recall the slope formula

The slope \(m\) of a line is given by \(m=\frac{\text{rise}}{\text{run}}\). If the slope is the same between any two points on a line, then \(\frac{\text{rise}_1}{\text{run}_1}=\frac{\text{rise}_2}{\text{run}_2}\).

Answer:

\(\frac{\text{rise}_1}{\text{run}_1}=\frac{\text{rise}_2}{\text{run}_2}\)