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The inequality shown is:

\[
y \leq 2x + 7
\]

### How to Graph the Inequality:

1. **Graph the boundary line**:  
   Since it's a "less than or equal to" (\(\leq\)) inequality, the boundary line is **solid**. The equation of the boundary line is \(y = 2x + 7\). This is a straight line with slope \(2\) and y-intercept \(7\).  
   - Start by plotting the point \((0, 7)\) on the y-axis.
   - Use the slope \(2\) (which means "rise 2, run 1") to find another point on the line. From \((0, 7)\), go up 2 units and to the right 1 unit to reach \((1, 9)\).
   - Draw a solid line through these points.

2. **Shade the appropriate region**:  
   The inequality is \(y \leq 2x + 7\), so we shade **below** the line. This represents all the points where \(y\) is less than or equal to \(2x + 7\).

Would you like further details or any additional explanation?

### Related Questions:
1. What does the slope and y-intercept represent in this equation?
2. How would the graph change if the inequality were \(y > 2x + 7\)?
3. Can you explain how to check if a point lies within the shaded region?
4. What does the "less than or equal to" symbol mean graphically?
5. How would you graph \(y \geq 2x + 7\)?

### Tip:
Always check the slope direction when plotting straight lines—it indicates how steeply the line rises or falls.

Graph the following inequality: y ≤ 2x + 7

Learn how to graph the inequality y ≤ 2x + 7 with a step-by-step guide. This includes plotting the boundary line and shading the region representing the solution. Suitable for students in Grades 7-9 studying algebra and inequalities.

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