Question

name

1. the graph of line a is shown. use the

similar slope triangles to compare the
slopes of segments gi and ik.

Explanation:

Step1: Recall the slope formula

The slope formula is \(m = \frac{\text{rise}}{\text{run}}\). For similar slope - triangles, the ratio of the vertical change (rise) to the horizontal change (run) is the same.

Step2: Calculate the slope for segment \(GI\)

Let's assume the coordinates (by counting the grid squares). Suppose \(G\) has coordinates \((x_1,y_1)\) and \(I\) has coordinates \((x_2,y_2)\). If we count the vertical change (rise) from \(G\) to \(I\) as \(y_2 - y_1=- 4\) (downward direction) and the horizontal change (run) as \(x_2 - x_1 = 1\). Then the slope \(m_{GI}=\frac{-4}{1}=-4\)

Step3: Calculate the slope for segment \(IK\)

Let's assume the coordinates of \(I\) and \(K\). If we count the vertical change (rise) from \(I\) to \(K\) as \(y_3 - y_2=- 8\) (downward direction) and the horizontal change (run) as \(x_3 - x_2 = 2\). Then the slope \(m_{IK}=\frac{-8}{2}=-4\)

Answer:

The slopes of segments \(GI\) and \(IK\) are equal. The slope of both segments is \(-4\)