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To graph the inequality \(4x - y \geq -3\), you can follow these steps:

1. **Rewrite the inequality** in slope-intercept form (i.e., \(y = mx + b\)) for easier graphing:
   \[
   y \leq 4x + 3
   \]

2. **Graph the line** \(y = 4x + 3\) first:
   - The slope \(m\) is 4, and the y-intercept \(b\) is 3.
   - Start by plotting the y-intercept at (0,3) and then use the slope to find another point (for example, go up 4 units and right 1 unit to reach (1,7)).

3. **Draw the line**: Since the inequality is \(\geq\), use a **solid line** to indicate that points on the line are included in the solution.

4. **Shade the region** above the line because the inequality is \(\geq\).

Would you like more detailed steps on graphing or additional examples? 

Here are some related questions:
1. How do we graph inequalities with different slopes and intercepts?
2. What changes when the inequality symbol is \(\leq\) or \(>\)?
3. How can we verify points that satisfy the inequality?
4. Why do we use solid lines for \(\geq\) or \(\leq\) inequalities?
5. How does shading indicate the solution region?

**Tip**: Always test a point (like (0,0)) to confirm the correct shaded region.

Understand how to graph the linear inequality 4x - y ≥ -3, including converting to slope-intercept form, graphing the line, and shading the appropriate region. This guide is suitable for high school students learning graphing techniques and solving inequalities.

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