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The inequality provided is \( y \leq 5 - 4x \). To find the correct graph, we will follow these steps:

1. **Identify the Line**: The line equation corresponding to the boundary of the inequality is \( y = 5 - 4x \).
2. **Plot the Line**: This line can be graphed by finding its intercepts:
   - **Y-intercept**: When \( x = 0 \), \( y = 5 \).
   - **X-intercept**: When \( y = 0 \), \( 5 - 4x = 0 \) leads to \( x = \frac{5}{4} \).

3. **Determine the Shaded Region**: The inequality is \( y \leq 5 - 4x \), which means the region below or on the line should be shaded.

4. **Check Graph Options**:
   - **Option A** shows a line with a negative slope and shading below the line.
   - **Option B** and **Option C** also show a line with a negative slope and shading below the line.

To distinguish between these, we need to ensure the slope and positioning match the equation \( y = 5 - 4x \). The slope of the line is \(-4\), and the line should pass through the points we identified above.

Upon close inspection:
- **Option A** matches the line equation and correctly shades the area below the line, including the boundary line itself (indicating \( \leq \) rather than \( < \)).

Thus, **Option A** is the correct representation of the inequality \( y \leq 5 - 4x \).

Would you like further explanation or have any questions? Here are some related questions to explore the topic further:

1. What are the characteristics of the line in the equation \( y = 5 - 4x \)?
2. How do you determine the shading for an inequality?
3. How can you find the x-intercept and y-intercept of a line?
4. What does the slope of a line indicate?
5. How can you verify if a point lies within the shaded region?
6. How would the graph change if the inequality were \( y < 5 - 4x \)?
7. How does the inequality \( y \geq 5 - 4x \) differ in its graphical representation?
8. What is the significance of the boundary line in graphing linear inequalities?

**Tip:** Always check if the inequality includes the boundary line (≤ or ≥) or not (< or >), as this determines if the line should be solid or dashed.

Understand how to graph the inequality y ≤ 5 - 4x step-by-step. This problem covers linear equations, inequalities, and graphing, including determining intercepts and shading regions correctly. Suitable for students in Grades 7-9.

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