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The graph shows a linear inequality with shading below a line, which indicates the region where the inequality holds. Let's analyze the line’s slope and y-intercept to write the inequality in slope-intercept form.

### Step-by-Step Solution:
1. **Identify two points on the line:** Looking at the line, two clear points are (0, -1) and (1, 0).
2. **Calculate the slope (m):** 
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-1)}{1 - 0} = 1
   \]
   So, the slope \( m = 1 \).
3. **Determine the y-intercept (b):** The line crosses the y-axis at -1, so \( b = -1 \).

The equation of the line is:
\[
y = x - 1
\]

4. **Determine the inequality symbol:** Since the shaded region is below the line, we use \( \leq \) (for “less than or equal to”) to include the boundary line.

### Final Answer:
The inequality is:
\[
y \leq x - 1
\]

Would you like further details or have any questions?

### Related Questions:
1. How do you determine if the inequality is \( \leq \) or \( \geq \) based on the shading?
2. What changes if the shaded region was above the line?
3. How would you solve for \( x \) if given an inequality in slope-intercept form?
4. What are the differences between linear inequalities and linear equations?
5. How would you graph \( y > x - 1 \) on a coordinate plane?

**Tip:** Always verify if the shaded region includes the boundary line by checking if the line is solid (for \( \leq \) or \( \geq \)) or dashed (for \( < \) or \( > \)).

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

Learn how to write a linear inequality in slope-intercept form based on a graph. This problem covers key algebraic concepts such as identifying slope, y-intercept, and determining the inequality symbol. Suitable for students in Grades 7-9.

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