To find the slope of a line through two points $(x_1, y_1)$ and $(x_2, y_2)$, we use the slope formula:

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

Given points $(8, 8)$ and $(3, 3)$, let:

• $(x_1, y_1) = (8, 8)$
• $(x_2, y_2) = (3, 3)$

Substitute these values into the formula:

$m = \frac{3 - 8}{3 - 8} = \frac{-5}{-5} = 1$

Thus, the slope of the line through the points $(8, 8)$ and $(3, 3)$ is:

$m = 1$

Would you like further details or have any questions?

Here are some related questions to deepen your understanding:

1. How does changing one of the points affect the slope calculation?
2. What does a slope of $1$ signify about the line's direction?
3. What would the slope be if the points were $(8, 3)$ and $(3, 8)$?
4. How would you calculate the slope if one point was at the origin?
5. Can you find the equation of the line that passes through these points?

Tip: When two points have the same $y$-value or $x$-value, the line is horizontal or vertical, respectively, and the slope will be zero or undefined.