The inequality given in the image is $y \leq -\frac{3}{4}x + 5$.

Steps to graph the inequality:

1. Plot the boundary line: The equation of the boundary line is $y = -\frac{3}{4}x + 5$. Since the inequality is $\leq$, the boundary line will be solid, meaning that points on the line are included in the solution.

   • The slope is $-\frac{3}{4}$, so for every 4 units you move to the right, you go down by 3 units.
   • The y-intercept is 5, so the line crosses the y-axis at $(0, 5)$.

2. Shade the region: Since the inequality is $y \leq -\frac{3}{4}x + 5$, you will shade the area below the line, where the y-values are less than or equal to the line.

Key Points:

• Start at $(0, 5)$ on the y-axis.
• Move according to the slope: down 3 and right 4 to plot additional points like $(4, 2)$ or $(-4, 8)$.
• Draw the solid line through these points.
• Shade below the line.

Do you need further details on any part of this? Let me know! Here are some follow-up questions:

1. Why is the line solid instead of dashed?
2. How do you determine which side of the line to shade?
3. What does the slope $-\frac{3}{4}$ represent in the context of this inequality?
4. How would the graph change if the inequality were $y > -\frac{3}{4}x + 5$?
5. Can you find the x-intercept of the boundary line?

Tip: Always remember that if the inequality sign is $\leq$ or $\geq$, the boundary line should be solid, while for $<$ or $>$, the line should be dashed.