1. **State the problem:** We are given two lines on a Cartesian plane and need to find the slope of the original line and the slope of a line perpendicular to it. 2. **Find the slope of the original line (green line):** The green line passes through points (-7, 2) and (-4, 8). The slope formula is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Substitute the points: $$m = \frac{8 - 2}{-4 - (-7)} = \frac{6}{3} = 2$$ So, the slope of the original line is $2$. 3. **Find the slope of the perpendicular line:** The slope of a line perpendicular to another is the negative reciprocal of the original slope. Since the original slope is $2$, the perpendicular slope is: $$m_{\perp} = -\frac{1}{2}$$ 4. **Check the blue line slope:** The blue line passes through points (-10, 7) and (10, -4). Calculate its slope: $$m = \frac{-4 - 7}{10 - (-10)} = \frac{-11}{20} = -\frac{11}{20}$$ This slope is not the negative reciprocal of $2$, so the blue line is not perpendicular to the green line. 5. **Summary:** - Original slope (green line): $2$ - Perpendicular slope: $-\frac{1}{2}$ You can graph a line with slope $-\frac{1}{2}$ to be perpendicular to the green line.