https://file.aiquickdraw.com/mathbot/file/1727045653608rt9mkhv3.jpg

The inequality given is:

\[
-5y \leq 2x + 10
\]

To graph the inequality, we first solve for \(y\).

### Step 1: Isolate \(y\)
Divide both sides by \(-5\), remembering to **flip the inequality sign** because we are dividing by a negative number:

\[
y \geq \frac{2x + 10}{-5}
\]

This simplifies to:

\[
y \geq -\frac{2}{5}x - 2
\]

### Step 2: Determine the line equation
The inequality represents a line with slope \(-\frac{2}{5}\) and a y-intercept of \(-2\). Since the inequality is \(y \geq -\frac{2}{5}x - 2\), the region above this line will be shaded, and the line itself will be solid (because the inequality includes "equal to").

### Step 3: Graphical Representation
- The slope is \(-\frac{2}{5}\), meaning for every 5 units you move to the right (along the x-axis), you move 2 units down.
- The y-intercept is \(-2\), meaning the line passes through the point \((0, -2)\).
- You would shade the area **above** this line because the inequality is \(y \geq\).

If you look at the options in the graph, you would find the one that:
1. Has a line with a negative slope of \(-\frac{2}{5}\).
2. Passes through the point \((0, -2)\).
3. Has a solid line.
4. The region above the line is shaded.

Let me know if you need further details or have any questions!

### Relative Questions:
1. What happens if the inequality had been \(y \leq -\frac{2}{5}x - 2\)?
2. How do we graph inequalities with dashed lines versus solid lines?
3. How can you find the slope of a line from its equation?
4. What is the effect of flipping the inequality when dividing by a negative number?
5. How do you check if a point satisfies an inequality?

### Tip:
Always remember to flip the inequality sign when multiplying or dividing both sides of an inequality by a negative number!

Which graph best represents the solution set to −5y ≤ 2x + 10?

Learn how to graph the inequality −5y ≤ 2x + 10 by solving for y and determining the line's slope and y-intercept. Explore step-by-step instructions on shading the correct region and understanding the rules for dividing by negative numbers in inequalities. Suitable for Grades 9-11.

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