https://file.aiquickdraw.com/mathbot/file/17271998125851k2adcxj.jpg

The graph you provided displays a linear inequality, and we are tasked with writing the inequality in slope-intercept form, which is generally expressed as:

\[
y \leq mx + b
\]
or
\[
y \geq mx + b
\]
depending on the shading of the graph.

### Steps to Determine the Inequality:

1. **Identify the boundary line**:
   The boundary line appears solid, meaning the inequality will include "≤" or "≥" (the solution set includes the boundary line).

2. **Find the slope**:
   The line passes through two distinct points:  
   - (0, 8)  
   - (8, 0)

   We can use these points to find the slope \( m \) using the slope formula:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 8}{8 - 0} = \frac{-8}{8} = -1
   \]

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

3. **Find the y-intercept**:
   The y-intercept \( b \) is the point where the line crosses the y-axis. From the graph, this happens at \( (0, 8) \), so \( b = 8 \).

4. **Write the equation of the boundary line**:
   Using the slope-intercept form of a line \( y = mx + b \):
   \[
   y = -x + 8
   \]

5. **Determine the inequality symbol**:
   The shading is below the boundary line, meaning the inequality is \( \leq \). Thus, the inequality that represents the graph is:

   \[
   y \leq -x + 8
   \]

### Final Inequality:
\[
y \leq -x + 8
\]

Would you like further clarification or details?

Here are five related questions to expand your understanding:
1. How do we interpret the shading in a linear inequality graph?
2. What happens if the boundary line is dashed instead of solid?
3. How do we handle cases where the slope is a fraction?
4. What is the significance of the y-intercept in a linear inequality?
5. Can you graph the inequality \( y \geq 2x - 3 \)?

**Tip:** When determining the slope from a graph, choose two points with integer coordinates to avoid calculation errors.

This is the graph of a linear inequality. Write the inequality in slope-intercept form.

Solve a linear inequality from a graph by determining the slope and y-intercept. Learn how to express the inequality in slope-intercept form. Suitable for Grades 7-10.

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