1. Let's analyze the hiker altitude problem first. The table shows hours hiked ($x$) vs altitude ($y$). Points: (1, 5650), (2, 5525), (3, 5400), (5, 5150), (8, 4775). 2. Calculate the rate of change (slope) $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5525 - 5650}{2 - 1} = \frac{-125}{1} = -125.$$ This means altitude decreases by 125 ft each hour. 3. Using point-slope form with point (1, 5650): $$y - 5650 = -125(x - 1) \implies y = -125x + 125 + 5650 = -125x + 5775.$$ 4. Now check the students' equations: - Mateo: $y = 125x + 5775$ (wrong slope, should be negative) - Julie: $y = -125x + 5775$ (correct) - Oliver: $y = -125x + 5650$ (wrong intercept) So, Julie wrote the correct equation. --- 5. Now for the reading problem: Table shows hours read ($x$) vs pages remaining ($y$). Points: (1, 644), (4, 500), (8, 308), (12, 116), (14, 20). 6. Calculate rate (pages per hour): Between (1, 644) and (4, 500): $$m = \frac{500 - 644}{4 - 1} = \frac{-144}{3} = -48.$$ The student reads at 48 pages per hour. Statement 9: True. 7. To find total pages, find intercept when $x=0$: Use $y = mx + b$, with $m = -48$, and point (1, 644): $$644 = -48(1) + b \implies b = 644 + 48 = 692.$$ So, total pages = 692. Statement 10: False (number given 644), correct statement: "Number of pages in the novel is 692." 8. Given $y = -48x + 692$, check if it fits data. At $x=1$: $y = -48(1) + 692 = 644$ matches table. So statement 11: True. Final answers: - 8. Correct equation by Julie: $y = -125x + 5775$ - 9. True - 10. False, correct total pages 692 - 11. True