To find the slope of the line passing through two points, we use the slope formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points.

Step 1: Assign the coordinates

• $(x_1, y_1) = (0, -7)$
• $(x_2, y_2) = (-4, 3)$

Step 2: Substitute into the slope formula

$m = \frac{3 - (-7)}{-4 - 0}$

$m = \frac{3 + 7}{-4}$

$m = \frac{10}{-4}$

$m = -\frac{5}{2}$

Step 3: Match with the options

Since $-\frac{5}{2} = -2.5$, it does not directly match any of the given options. It seems there may be an error in the problem or the choices provided. Let me verify further if there is additional context or information you may want clarified.

Would you like to double-check this setup or adjust the numbers for clarity?

5 Questions for Exploration:

1. How does the slope change if we reverse the order of points?
2. Can you graph these points to verify the line visually?
3. How do we calculate slope for vertical or horizontal lines?
4. Why is the denominator in the slope formula crucial?
5. What happens to the slope if both $x$ and $y$ coordinates decrease?

Tip: Always reduce fractions to their simplest form when finding slopes for clarity.