https://file.aiquickdraw.com/mathbot/file/1728253086916lyz6dfwy.jpg

The inequality given is:

\[
y > -\frac{6}{7}x
\]

### Steps to Graph the Inequality:
1. **Graph the boundary line**: 
   - The inequality has a slope of \(-\frac{6}{7}\) and no y-intercept term (which means the line passes through the origin \((0, 0)\)).
   - Since the inequality is "greater than" (not "greater than or equal to"), use a dashed line to represent the boundary because points on the line itself are not included in the solution.

2. **Choose a test point**:
   - Select a point that is not on the boundary line to test which side of the line to shade. A common choice is \((0, 0)\), but since this point is on the line, choose another, like \((0, 1)\).

3. **Test the inequality with the test point**:
   - Substitute \((0, 1)\) into the inequality:
     \[
     1 > -\frac{6}{7}(0) \quad \Rightarrow \quad 1 > 0
     \]
     This is true, so the region containing \((0, 1)\) is part of the solution.

4. **Shade the region**:
   - Shade the area above the line because the inequality is \(y > -\frac{6}{7}x\). This region represents all points where the y-values are greater than the line values.

Would you like a detailed graphical representation, or do you have any questions? 

### Related Questions:
1. How would the graph change if the inequality were \(y \geq -\frac{6}{7}x\)?
2. What happens if the slope is positive instead of negative?
3. How do you handle inequalities with a non-zero y-intercept?
4. How do you determine which side of the line to shade in more complex inequalities?
5. What is the significance of a dashed versus a solid line in inequality graphs?

### Tip:
Always choose a test point away from the boundary to easily check which region to shade.

Learn how to graph the linear inequality y > -6/7x. This guide explains step-by-step how to plot the boundary line with a negative slope, choose a test point, and shade the correct region. Perfect for students in Grades 7-10 studying linear inequalities.

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