1. **State the problem:** We have a scatter plot showing the relationship between time spent watching TV (x) and time spent doing homework (y). We want to find the line of best fit (a linear equation) and then use it to predict homework time for 12 hours of TV. 2. **Formula for line of best fit:** The line is generally written as $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Estimate slope ($m$):** From the scatter plot, as $x$ increases, $y$ decreases, indicating a negative slope. Using two approximate points from the graph, for example: - Point A: $(0, 28)$ - Point B: $(28, 4)$ Calculate slope: $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 28}{28 - 0} = \frac{-24}{28} = -0.8571 \approx -0.86$$ 4. **Find y-intercept ($b$):** Using point A $(0, 28)$: $$b = y - mx = 28 - (-0.86)(0) = 28$$ 5. **Equation of line:** $$y = -0.86x + 28$$ 6. **Predict homework time for 12 hours TV:** Substitute $x=12$: $$y = -0.86(12) + 28 = -10.32 + 28 = 17.68$$ 7. **Final answers:** (a) Line of best fit: $$y = -0.86x + 28$$ (b) Predicted homework time for 12 hours TV: $$17.68$$ hours