Question

find the slope of the line using similar triangles.
a. find rise over run for triangle mnp. type your answer.
b. find rise over run for triangle jkl. type your answer.
c. simplify the ratio for abc. type your answer.
d. what is the slope of the line? type your answer.

Explanation:

Step1: Define rise - over - run for triangle MNP

For triangle MNP, assume two points on the line within the triangle. Let's say the vertical change (rise) from one point to another is - 3 (going down) and the horizontal change (run) is 2 (going to the right). So the rise - over - run is $\frac{-3}{2}$.

Step2: Define rise - over - run for triangle JKL

For triangle JKL, if we consider two points on the line within the triangle, the vertical change (rise) is - 6 (going down) and the horizontal change (run) is 4 (going to the right). So the rise - over - run is $\frac{-6}{4}=-\frac{3}{2}$.

Step3: Simplify the ratio

The ratio for both triangles is already in simplest form for the non - simplified cases. For the general concept related to the line, the slope is the same for similar triangles formed on a straight line.

Step4: Determine the slope of the line

Since the rise - over - run (slope) is the same for similar triangles on a line, the slope of the line is $-\frac{3}{2}$.

Answer:

A. $-\frac{3}{2}$
B. $-\frac{3}{2}$
C. $-\frac{3}{2}$
D. $-\frac{3}{2}$