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Let's work through the slope calculations for each pair of points using the slope formula:

\[
\text{Slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
\]

### 1. Points: (5, -3) and (-1, 6)
\[
\Delta y = 6 - (-3) = 6 + 3 = 9
\]
\[
\Delta x = -1 - 5 = -6
\]
\[
\text{Slope} = \frac{9}{-6} = -\frac{3}{2}
\]

### 2. Points: (7, 11) and (4, 8)
\[
\Delta y = 8 - 11 = -3
\]
\[
\Delta x = 4 - 7 = -3
\]
\[
\text{Slope} = \frac{-3}{-3} = 1
\]

### 3. Points: (1, 4) and (7, -2)
\[
\Delta y = -2 - 4 = -6
\]
\[
\Delta x = 7 - 1 = 6
\]
\[
\text{Slope} = \frac{-6}{6} = -1
\]

### 4. Points: (-6, 4) and (2, 9)
\[
\Delta y = 9 - 4 = 5
\]
\[
\Delta x = 2 - (-6) = 2 + 6 = 8
\]
\[
\text{Slope} = \frac{5}{8}
\]

### 5. Points: (-8, 2) and (3, 5)
\[
\Delta y = 5 - 2 = 3
\]
\[
\Delta x = 3 - (-8) = 3 + 8 = 11
\]
\[
\text{Slope} = \frac{3}{11}
\]

### 6. Points: (-5, 3) and (1, 10)
\[
\Delta y = 10 - 3 = 7
\]
\[
\Delta x = 1 - (-5) = 1 + 5 = 6
\]
\[
\text{Slope} = \frac{7}{6}
\]

### 7. Points: (-2, -3) and (-7, -1)
\[
\Delta y = -1 - (-3) = -1 + 3 = 2
\]
\[
\Delta x = -7 - (-2) = -7 + 2 = -5
\]
\[
\text{Slope} = \frac{2}{-5} = -\frac{2}{5}
\]

### 8. Points: (0, 1) and (4, 9)
\[
\Delta y = 9 - 1 = 8
\]
\[
\Delta x = 4 - 0 = 4
\]
\[
\text{Slope} = \frac{8}{4} = 2
\]

Would you like further clarification on any of the calculations? 

Here are five related questions:
1. How would the slope change if the points were reversed?
2. What does the slope represent in a real-world context?
3. How can you interpret the slope of 0 or an undefined slope?
4. What do positive and negative slopes signify about the direction of a line?
5. How can you calculate the equation of a line once you have the slope and one point?

**Tip**: Always double-check signs when subtracting negative numbers to avoid common mistakes!

Find the slope of a line that passes through the given two points using the ratio method.

Learn how to calculate the slope of a line using the ratio method with two given points. Detailed step-by-step solutions are provided for each problem, covering key concepts in algebra and linear equations. Suitable for students in Grades 8-10.

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