Let's break down the problem based on the graph shown. The task asks to "describe and find the slope of the line" passing through the points $(-3, 1)$ and $(2, -2)$.

To find the slope:

1. The slope $m$ of a line is given by the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Where:

   • $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line.

2. Using the points $(-3, 1)$ and $(2, -2)$:

   • $(x_1, y_1) = (-3, 1)$
   • $(x_2, y_2) = (2, -2)$

3. Substitute these values into the slope formula: $m = \frac{-2 - 1}{2 - (-3)} = \frac{-3}{5}$ Therefore, the slope of the line is $-\frac{3}{5}$.

Description:

This line has a negative slope, indicating it is slanting downward from left to right. The slope, $-\frac{3}{5}$, means that for every 5 units the line moves horizontally to the right, it moves 3 units downward.

Slope: $-\frac{3}{5}$

Would you like more details or have any further questions?

Here are some related questions you could explore:

1. How do we interpret a negative slope geometrically?
2. What is the meaning of a slope of 0 in a line?
3. Can the slope of a vertical line be calculated? If yes, what is it?
4. How does the slope relate to the angle of inclination of a line?
5. How would the slope change if we switched the points $(2, -2)$ and $(-3, 1)$?

Tip: The slope is a measure of how steep a line is. The larger the absolute value of the slope, the steeper the line.