https://file.aiquickdraw.com/mathbot/file/1727285677332bgii8e2p.jpg

The graph represents a line passing through the points \((-4, 2)\) and \((0, -3)\). Based on this information, we can find the equation of the line and then use it to determine the inequality.

### Step 1: Find the slope
The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substitute the points \((-4, 2)\) and \((0, -3)\):
\[
m = \frac{-3 - 2}{0 - (-4)} = \frac{-5}{4}
\]
So, the slope of the line is \( m = -\frac{5}{4} \).

### Step 2: Use the point-slope form to write the equation
The point-slope form of a line is:
\[
y - y_1 = m(x - x_1)
\]
Using the point \((0, -3)\) and the slope \( m = -\frac{5}{4} \), we get:
\[
y - (-3) = -\frac{5}{4}(x - 0)
\]
Simplifying:
\[
y + 3 = -\frac{5}{4}x
\]
\[
y = -\frac{5}{4}x - 3
\]
This is the equation of the line.

### Step 3: Determine the inequality
The shaded region in the graph lies **below** the line, which means the inequality is:
\[
y \leq -\frac{5}{4}x - 3
\]
The inequality includes the line itself (since it is dashed) and the region below it.

### Final Answer:
\[
y \leq -\frac{5}{4}x - 3
\]

Would you like a detailed explanation of any part of this process, or have further questions on inequalities?

Here are some related questions to explore:
1. How do you find the slope of a line from a graph?
2. What is the difference between a dashed and solid line in inequalities?
3. How can you determine whether to use \(\leq\) or \(<\) in inequalities from a graph?
4. How would the inequality change if the shaded region were above the line?
5. What does the slope tell you about the direction of the line?

**Tip:** When analyzing graphs, always pay attention to the shading, which helps indicate whether the inequality involves "greater than" or "less than."

Write an inequality that represents the graph.

Learn how to write an inequality from a graph by analyzing the slope, intercept, and shaded region. This problem involves finding the inequality y ≤ -(5/4)x - 3 based on a line passing through two points. Suitable for students in Grades 8-10.

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