The inequality you provided is:

\[
y \leq \frac{6}{5}x - 4
\]

This describes a region on the coordinate plane.

### Step-by-Step Explanation:
1. **Slope and y-intercept**: 
   - The slope of the line is \(\frac{6}{5}\), meaning for every 5 units you move to the right along the x-axis, you move 6 units up along the y-axis.
   - The y-intercept is \(-4\), so the line crosses the y-axis at the point \((0, -4)\).

2. **Graphing the line**:
   - The line \(y = \frac{6}{5}x - 4\) is a straight line with a slope of \(\frac{6}{5}\) and a y-intercept of \(-4\). You would plot this line using these two pieces of information.
   - Since the inequality is \(\leq\) (less than or equal to), the line itself is **included** in the solution, so it should be drawn as a solid line.

3. **Shading the region**:
   - The inequality indicates that we want the region **below** or **on** the line because it is \(y \leq \frac{6}{5}x - 4\).
   - To determine this, pick a test point not on the line, such as \((0, 0)\). Plugging this into the inequality:
     \[
     0 \leq \frac{6}{5}(0) - 4 \quad \Rightarrow \quad 0 \leq -4
     \]
     This is false, so the point \((0, 0)\) is **not** part of the solution. Therefore, the region **below the line** is the solution.

### Do you have any further questions, or would you like a graphical representation?

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Here are 5 related questions to explore:
1. How do you graph inequalities with a different slope or y-intercept?
2. What happens if the inequality is \(y \geq \frac{6}{5}x - 4\)?
3. How do you graph systems of linear inequalities?
4. What is the significance of the test point method in graphing inequalities?
5. How do inequalities change when you multiply or divide by a negative number?

**Tip**: Always use a test point to confirm which region of the graph to shade when dealing with inequalities.

Understand how to solve and graph the linear inequality y ≤ 6/5x - 4 using slope-intercept form. Explore concepts such as graphing, the slope-intercept theorem, and the test point method. This explanation is designed for students in Grades 8-10.

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