Question

Which is the graph of the solution set of the inequality 3x−4y≤24
?(1 point)
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Answer 1

To solve the inequality \( 3x - 4y \leq 24 \), we can first rewrite it in slope-intercept form (y = mx + b) to determine the line and the shading required for the solution set.

1. Start with the inequality:
\[
3x - 4y \leq 24
\]

2. Rearrange it to solve for \( y \):
\[
-4y \leq -3x + 24
\]

3. Divide each term by -4 (remember to reverse the inequality when dividing by a negative):
\[
y \geq \frac{3}{4}x - 6
\]

Now, we have the line \( y = \frac{3}{4}x - 6 \).

### Steps to Graph:
- The y-intercept is -6 (where the line crosses the y-axis).
- The slope is \(\frac{3}{4}\), meaning for every 4 units you move right (along the x-axis), you move up 3 units (along the y-axis).

Now, since the inequality is \( y \geq \frac{3}{4}x - 6 \), we will:
- Draw a dashed line for \( y = \frac{3}{4}x - 6 \) (because the inequality sign is not \(\leq\), meaning points on the line are not included).
- Shade above the line to indicate where \( y \) is greater than or equal to the line.

### Summary:
1. Graph the line \( y = \frac{3}{4}x - 6 \) with a dashed line.
2. Shade above this line to represent the solution set for the inequality \( 3x - 4y \leq 24 \).

If you have response options available, look for the graph with a dashed line passing through the y-intercept at -6, with shading above the line.