1. The problem asks to find the slope of a line given the "rise" and "run" segments on a Cartesian plane. 2. The slope formula is: $$\text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\Delta y}{\Delta x}$$ where $\Delta y$ is the vertical change (rise) and $\Delta x$ is the horizontal change (run). 3. From the graph description, the line goes from approximately $(0,6)$ to $(8,0)$. 4. Calculate the rise: $$\Delta y = y_2 - y_1 = 0 - 6 = -6$$ 5. Calculate the run: $$\Delta x = x_2 - x_1 = 8 - 0 = 8$$ 6. Substitute into the slope formula: $$\text{slope} = \frac{-6}{8}$$ 7. Simplify the fraction by dividing numerator and denominator by their greatest common divisor 2: $$\text{slope} = \frac{\cancel{ -6 }^{\div 2}}{\cancel{ 8 }^{\div 2}} = \frac{-3}{4}$$ 8. The slope of the line in simplest form is: $$\boxed{-\frac{3}{4}}$$ This means for every 4 units you move horizontally to the right (run), the line goes down 3 units (rise), indicating a negative slope.