https://file.aiquickdraw.com/mathbot/file/1727452960158o0qajo4p.jpg

The graph shown in your image represents a two-variable inequality, and I'll help you analyze it to determine the correct inequality. From the image, we observe the following:

- The line appears to have a negative slope, passing through points like \((0, 3)\) and \((3, 0)\), which allows us to determine its equation.
- The region below the line is shaded, indicating that the inequality likely involves \( \leq \) or \( < \).

### Step 1: Find the equation of the line
We can use the slope-intercept form of a line, which is:

\[
y = mx + b
\]

where:
- \(m\) is the slope of the line.
- \(b\) is the y-intercept.

#### Find the slope:
Using the points \((0, 3)\) and \((3, 0)\):
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 3}{3 - 0} = -1
\]

Thus, the slope \(m = -1\).

#### Equation of the line:
The y-intercept \(b = 3\) (since the line passes through \((0, 3)\)). Therefore, the equation of the line is:
\[
y = -x + 3
\]

### Step 2: Determine the inequality
Since the shaded region is below the line, this represents the area where the y-values are less than or equal to the line. The inequality is:

\[
y \leq -x + 3
\]

This is the inequality represented by the graph.

Would you like further details or explanations?

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Here are 5 related questions:
1. How do you graph inequalities on a coordinate plane?
2. What happens if the region above the line is shaded?
3. How can you determine whether the inequality is strict (< or >) or non-strict (≤ or ≥)?
4. What is the role of the slope and y-intercept in determining a line's equation?
5. How do you convert between the standard form of a line and slope-intercept form?

**Tip**: When graphing inequalities, remember that a dashed line represents strict inequalities (< or >), while a solid line represents non-strict inequalities (≤ or ≥).

Find the inequality represented by the graph on Khan Academy showing a line with a negative slope and a shaded region below the line.

Learn how to find the inequality represented by a graph where the line has a negative slope and the region below the line is shaded. This problem covers key algebraic concepts such as slope, y-intercept, and inequalities. Suitable for students in Grades 8-10.

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