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

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

where:

• $(x_1, y_1) = (7, -5)$
• $(x_2, y_2) = (3, -1)$

Let's substitute the values:

$m = \frac{-1 - (-5)}{3 - 7} = \frac{-1 + 5}{3 - 7} = \frac{4}{-4} = -1$

Answer:

The slope of the line through the points $(7, -5)$ and $(3, -1)$ is $-1$.

Would you like a deeper explanation or have any questions?

Here are some related questions you might find interesting:

1. What is the equation of the line through these points?
2. How do you find the slope if given two points in a different format?
3. What does a negative slope mean in terms of the line's direction?
4. Can the slope formula be used in three-dimensional space?
5. How would the slope change if one of the points were different?

Tip: Remember that a negative slope means the line goes downward from left to right.