https://file.aiquickdraw.com/mathbot/file/1726336405982xfmu2mrq.jpg

https://file.aiquickdraw.com/mathbot/file/17263364059821xaw85b3.jpg

The given graph shows a linear inequality. The line in the graph has a slope of \(\frac{4}{3}\) and a y-intercept of \(-2\), as seen in the equation \(y = \frac{4}{3}x - 2\). 

Now, let's analyze the shading and the type of line:
- The line is dashed, indicating that points on the line are **not** included in the solution, so the inequality will be either "<" or ">".
- The shaded region is above the line, which implies that the inequality represents \(y > \frac{4}{3}x - 2\).

Thus, the correct inequality for the graph is:
\[
\boxed{D. \, y > \frac{4}{3}x - 2}
\]

Would you like more details on the reasoning, or have any questions about this solution? Here are some related questions to consider:

1. What would change in the inequality if the line were solid instead of dashed?
2. How do you determine which side of the line is shaded in an inequality graph?
3. Why does the slope \(\frac{4}{3}\) matter for determining the inequality equation?
4. What happens if you swap the inequality sign from ">" to "<" in terms of the shaded region?
5. Can you explain how the y-intercept influences the inequality?

**Tip:** Always pay attention to whether the line in the graph is dashed or solid, as it affects whether the inequality includes an equal sign (≥ or ≤).

This graph shows the solution to which inequality?

This problem demonstrates how to solve a linear inequality by analyzing the graph. The inequality is y > (4/3)x - 2, and the graph is shaded above the dashed line, meaning points on the line are not included in the solution. Suitable for Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation