Let’s go through each question step-by-step to ensure all parts are answered.

Questions 1-3: Finding the Slope

The slope formula is: $\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}$

1. For points (6, 5) and (3, 7.5):

   • $\text{slope} = \frac{7.5 - 5}{3 - 6} = \frac{2.5}{-3} = -\frac{5}{6}$

2. For points (12, -10) and (15, -8):

   • $\text{slope} = \frac{-8 - (-10)}{15 - 12} = \frac{-8 + 10}{3} = \frac{2}{3}$

3. For points (1, 4) and (0, 11):

   • $\text{slope} = \frac{11 - 4}{0 - 1} = \frac{7}{-1} = -7$

Question 4: Checking Madeline's Work

Madeline calculates the slope between the points (9, 12) and (7, 4) as follows: $\frac{12 - 4}{7 - 9} = \frac{8}{-2} = -4$ Her setup and calculation are correct because she has properly subtracted $y$-values and $x$-values in the correct order.

Question 5: Slope of $\frac{5}{3}$

We need to find which point option has a slope of $\frac{5}{3}$.

1. Option D: (5, 7) and (10, 10) seems correct because:
   • $\text{slope} = \frac{10 - 7}{10 - 5} = \frac{3}{5} = \frac{5}{3}$