To graph the inequality \(4 > z\), we treat \(z\) as the variable on the vertical axis (often labeled as \(y\)).

1. **Step 1: Draw the boundary line.**
   - The inequality \(4 > z\) can be rewritten as \(z < 4\). This means that the variable \(z\) (or \(y\)) should be less than 4.
   - First, graph the line \(z = 4\), which is a **horizontal line** at \(y = 4\).
   - Since this inequality is strict (does not include \(z = 4\)), the line should be **dashed**, indicating that points on the line itself are not included in the solution.

2. **Step 2: Shade the appropriate region.**
   - Since \(z\) is less than 4, the region **below** the dashed line \(y = 4\) should be shaded. This shaded area represents all the points where \(z\) is less than 4.

Thus, the graph is a horizontal dashed line at \(y = 4\) with the area below the line shaded.

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Would you like more details on graphing inequalities or any further clarifications? Here are five related questions to expand your understanding:

1. How do we graph inequalities with two variables (e.g., \(y > 2x + 3\))?
2. What changes when the inequality is \( \geq \) instead of \( > \)?
3. Can we solve inequalities with absolute values graphically?
4. How do we solve a system of inequalities on a graph?
5. How does the graph change when inequalities involve quadratic functions?

**Tip**: When graphing inequalities, always pay attention to whether the inequality is strict (e.g., \(<\)) or inclusive (e.g., \(\leq\)). This determines whether the boundary line is dashed or solid.

Learn how to graph the inequality 4 > z by plotting a dashed horizontal line at y = 4 and shading the region below it. This guide walks through each step, helping students understand inequalities and graphing concepts. Suitable for Grades 7-10.

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