Question

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 a line segment between two points \((x_1,y_1)\) and \((x_2,y_2)\), \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For similar slope - triangles, if \(\triangle_1\) and \(\triangle_2\) are similar, the ratios of their corresponding sides are equal.

Step2: Calculate the slope of \(GI\)

Let's assume the side lengths of the slope - triangle for \(GI\). If the vertical change (rise) for \(GI\) is \(a\) and the horizontal change (run) is \(b\), then the slope of \(GI\), \(m_{GI}=\frac{a}{b}\).

Step3: Calculate the slope of \(IK\)

Since the slope - triangles for \(GI\) and \(IK\) are similar. Let the vertical change (rise) for \(IK\) be \(ka\) (where \(k\) is the scale factor of similarity) and the horizontal change (run) be \(kb\). Then the slope of \(IK\), \(m_{IK}=\frac{ka}{kb}\).
Simplify \(m_{IK}=\frac{ka}{kb}=\frac{a}{b}\) (since \(k
eq0\)).

Answer:

The slope of segment \(GI\) is equal to the slope of segment \(IK\).