To calculate the slopes of each line in the graph, we'll use the slope formula:

$\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}$

Each line has two labeled points, which allows us to apply this formula to find the slope.

Line A (Blue Line)

Given points: $(2, 6)$ and $(8, 4)$ $\text{slope of A} = \frac{4 - 6}{8 - 2} = \frac{-2}{6} = -\frac{1}{3}$

Line B (Green Line)

Given points: $(-5, 7)$ and $(1, 1)$ $\text{slope of B} = \frac{1 - 7}{1 - (-5)} = \frac{-6}{6} = -1$

Line C (Purple Line)

Given points: $(-6, -3)$ and $(-2, -8)$ $\text{slope of C} = \frac{-8 - (-3)}{-2 - (-6)} = \frac{-5}{4} = -\frac{5}{4}$

Summary of Slopes

• Slope of Line A: $-\frac{1}{3}$
• Slope of Line B: $-1$
• Slope of Line C: $-\frac{5}{4}$

Would you like further details or explanations on any of these calculations?

Here are some follow-up questions to deepen your understanding:

1. How does the slope affect the steepness and direction of each line?
2. What would the slope be if two points on the line were reversed?
3. Can you determine the y-intercept of each line using these points?
4. How would the graph look if each line's slope were doubled?
5. What happens to the slope if one point is shifted vertically by a constant amount?

Tip: When calculating slope, always ensure you subtract consistently (e.g., $y_2 - y_1$ and $x_2 - x_1$) to avoid sign errors.