1. **Problem 7: Find the equation of the line on the graph.** The graph shows a line descending from left to right, crossing the y-axis at approximately 3.5 and the x-axis at approximately 3.5. 2. **Formula and rules:** The equation of a line in slope-intercept form is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Find the slope $m$: ** Slope $m = \frac{\text{change in } y}{\text{change in } x} = \frac{0 - 3.5}{3.5 - 0} = \frac{-3.5}{3.5} = -1$ 4. **Write the equation:** Since the y-intercept $b = 3.5$, the equation is $$y = -1x + 3.5$$ or simply $$y = -x + 3.5$$ --- 5. **Problem 8: Write an equation modeling the cheetah's distance $y$ in feet after $x$ seconds.** Given data: | Time $x$ (seconds) | Distance $y$ (feet) | |--------------------|---------------------| | 5 | 477.5 | | 10 | 954.5 | | 15 | 1411.5 | | 20 | 1886.5 | | 25 | 2355.0 | 6. **Check if the relationship is linear:** Calculate the ratio $\frac{y}{x}$ for each pair: - $\frac{477.5}{5} = 95.5$ - $\frac{954.5}{10} = 95.45$ - $\frac{1411.5}{15} = 94.1$ - $\frac{1886.5}{20} = 94.325$ - $\frac{2355.0}{25} = 94.2$ The ratios are approximately constant, so the relationship is roughly linear. 7. **Find the average rate (speed):** Average speed $m \approx 95$ feet per second. 8. **Write the equation:** $$y = 95x$$ --- 9. **Problem 9: Nolan's salary varies directly with hours worked.** Given: - Salary $S_1 = 3202.33$ for $h_1 = 33.5$ hours - Find salary $S_2$ for $h_2 = 40$ hours 10. **Direct variation formula:** $$S = kh$$ where $k$ is the constant of proportionality. 11. **Find $k$: ** $$k = \frac{S_1}{h_1} = \frac{3202.33}{33.5} \approx 95.55$$ 12. **Calculate $S_2$: ** $$S_2 = k h_2 = 95.55 \times 40 = 3822$$ --- 13. **Problem 10: Which statements are proportional?** - I. Babysitter charges 7.50 per hour — proportional (constant rate) - II. Caterers charge 6 per dinner plus 2 delivery fee — not proportional (fixed fee) - III. Library charges 0.15 per day — proportional (constant rate) - IV. Roses cost 4.25 per rose plus 10 cutting fee — not proportional (fixed fee) **Answer:** Statements I and III are proportional. --- 14. **Problem 11: Scatterplot calories vs calories from fat.** If a meal has 250 calories from fat, estimate total calories. From the scatterplot description, calories from fat and total calories have a positive correlation. Assuming linear relation, approximate total calories for 250 calories from fat is about 500 calories (midpoint estimate from graph range). --- 15. **Problem 12: Find the mean absolute deviation of pets data:** Data: 3, 6, 2, 3, 4, 2, 3 16. **Calculate mean:** $$\text{mean} = \frac{3 + 6 + 2 + 3 + 4 + 2 + 3}{7} = \frac{23}{7} \approx 3.29$$ 17. **Calculate absolute deviations:** |3 - 3.29| = 0.29 |6 - 3.29| = 2.71 |2 - 3.29| = 1.29 |3 - 3.29| = 0.29 |4 - 3.29| = 0.71 |2 - 3.29| = 1.29 |3 - 3.29| = 0.29 18. **Mean absolute deviation:** $$\frac{0.29 + 2.71 + 1.29 + 0.29 + 0.71 + 1.29 + 0.29}{7} = \frac{6.87}{7} \approx 0.98$$ **Final answers:** - Problem 7: $$y = -x + 3.5$$ - Problem 8: $$y = 95x$$ - Problem 9: Nolan's salary for 40 hours is approximately 3822 - Problem 10: Statements I and III are proportional - Problem 11: Estimated total calories for 250 calories from fat is about 500 - Problem 12: Mean absolute deviation is approximately 0.98