1. **Problem 7:** Find the slope-intercept form of the line graphed on the coordinate plane. 2. **Step 1: Identify two points on the line.** Since the graph is not provided, assume two points from the grid, for example, $(0, y_1)$ and $(x_2, y_2)$. 3. **Step 2: Calculate the slope $m$.** The slope formula is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 4. **Step 3: Use the slope-intercept form formula.** The slope-intercept form is $$y = mx + b$$ where $b$ is the y-intercept. 5. **Step 4: Find $b$ by substituting one point into the equation.** Substitute $x$ and $y$ from one point and solve for $b$. 6. **Step 5: Write the final equation.** Since the graph is not visible, the exact equation cannot be determined here. --- 7. **Problem 8 Part A:** Find initial cost and hourly rate of Carpenter L from the table: Hours $h$: 1, 2, 3 Cost $c$: 187, 259, 331 8. **Step 1: Calculate hourly rate (slope).** $$m = \frac{259 - 187}{2 - 1} = \frac{72}{1} = 72$$ 9. **Step 2: Calculate initial cost (y-intercept).** Use $c = mh + b$ with $h=1$, $c=187$: $$187 = 72 \times 1 + b \Rightarrow b = 187 - 72 = 115$$ 10. **Answer Part A:** Initial cost = 115 Rate per hour = 72 11. **Problem 8 Part B:** Write equation for Carpenter L cost function. $$c = 72h + 115$$ 12. **Problem 8 Part C:** Compare cost for 6 hours with Carpenter N. Carpenter N cost: $$c_N = 60 \times 6 + 195 = 360 + 195 = 555$$ Carpenter L cost: $$c_L = 72 \times 6 + 115 = 432 + 115 = 547$$ Difference: $$555 - 547 = 8$$ 13. **Problem 9:** Write slope-intercept form for slope $-\frac{5}{8}$ passing through $(-14, 6)$. 14. **Step 1: Use point-slope form:** $$y - y_1 = m(x - x_1)$$ $$y - 6 = -\frac{5}{8}(x + 14)$$ 15. **Step 2: Simplify:** $$y - 6 = -\frac{5}{8}x - \frac{5}{8} \times 14$$ $$y - 6 = -\frac{5}{8}x - \frac{70}{8}$$ $$y - 6 = -\frac{5}{8}x - 8.75$$ 16. **Step 3: Solve for $y$:** $$y = -\frac{5}{8}x - 8.75 + 6$$ $$y = -\frac{5}{8}x - 2.75$$ 17. **Answer:** $$y = -\frac{5}{8}x - 2.75$$ 18. **Problem 10 Part A:** Plot tennis ball height data points: Bounces $x$: 1, 2, 3, 4 Heights $y$: 8, 6, 2, 1 19. **Plot points:** (1,8), (2,6), (3,2), (4,1) on coordinate plane. **Final answers:** - Problem 7: Cannot determine exact equation without graph. - Problem 8A: Initial cost = 115, Rate per hour = 72 - Problem 8B: $c = 72h + 115$ - Problem 8C: Difference in cost for 6 hours = 8 - Problem 9: $y = -\frac{5}{8}x - 2.75$ - Problem 10A: Plot points (1,8), (2,6), (3,2), (4,1)