Question

1. use similar right triangles to determine the slope of each line.

Explanation:

Step1: Recall the slope formula

The slope \(m\) of a line is given by \(m=\frac{\text{rise}}{\text{run}}\). For similar right - triangles, the ratio of the vertical side (rise) to the horizontal side (run) is the same for a given line.

Step2: Analyze the steeper line

For the steeper line, if we consider a right - triangle formed by the line. Let's assume two points on the steeper line. Suppose we move from \((- 4,6)\) to \((0, - 6)\). The rise is \(-6 - 6=-12\) and the run is \(0-(-4) = 4\). So the slope \(m_1=\frac{-12}{4}=-3\).

Step3: Analyze the less - steep line

For the less - steep line, assume two points, say \((0,-3)\) and \((8,0)\). The rise is \(0 - (-3)=3\) and the run is \(8 - 0=8\). So the slope \(m_2=\frac{3}{8}\).

Answer:

The slopes of the lines are \(-3\) and \(\frac{3}{8}\)