https://file.aiquickdraw.com/mathbot/file/1727927153557hdw3jqdp.jpg

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?

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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.

Describe and find the slope of the line passing through the points (-3, 1) and (2, -2).

Learn how to calculate the slope of a line passing through the points (-3, 1) and (2, -2) using the slope formula. This problem explores key concepts in algebra and coordinate geometry, suitable for students in Grades 8-10.

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