Question

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

Explanation:

Step1: Define rise - over - run for LKJ

Count vertical and horizontal units. For triangle LKJ, if we assume each grid square is 1 unit, moving from J to K (horizontal - run) is 2 units and from K to L (vertical - rise) is - 3 units. So the rise - over - run is $\frac{-3}{2}$.

Step2: Define rise - over - run for PNM

Moving from N to M (horizontal - run) is 4 units and from P to N (vertical - rise) is - 6 units. So the rise - over - run is $\frac{-6}{4}$.

Step3: Simplify the ratio for PNM

Simplify $\frac{-6}{4}$ by dividing both numerator and denominator by 2. We get $\frac{-3}{2}$.

Step4: Determine the slope of the line

Since the two triangles are similar and the rise - over - run (slope) is the same for similar right - triangles formed by the line, the slope of the line is $\frac{-3}{2}$.

Answer:

A. $\frac{-3}{2}$
B. $\frac{-6}{4}$
C. $\frac{-3}{2}$
D. $\frac{-3}{2}$