https://file.aiquickdraw.com/mathbot/file/1730398867430jt3gkc9i.jpg

To determine the correct inequality represented by the graph, we need to analyze the line equation, the direction of shading, and the type of line (dashed or solid).

1. **Identify the Slope and Y-Intercept of the Line:**
   - The line has a negative y-intercept at \(-3\) (where it crosses the y-axis), suggesting the form \( y = mx - 3 \).
   - The slope of the line can be estimated by finding two points on the line. It appears that from \((0, -3)\) to \((3, 2)\), there is a rise of 5 units and a run of 3 units. This gives a slope \( m = \frac{5}{3} \).

   Thus, the line equation is approximately:
   \[
   y = \frac{5}{3}x - 3
   \]

2. **Determine the Shading and Type of Inequality:**
   - The graph is shaded below the line, which suggests a "less than" inequality.
   - Since the line is dashed, it indicates a strict inequality (i.e., "<" or ">") without "or equal to".

3. **Conclusion:**
   - The inequality that represents the graph is:
     \[
     y < \frac{5}{3}x - 3
     \]

So, the correct answer is:
**\( y < \frac{5}{3}x - 3 \)**.

Would you like further details, or do you have any questions?

### Additional Questions:
1. What does the slope of a line indicate in an inequality graph?
2. How can you identify the correct inequality when the line is solid rather than dashed?
3. What is the significance of shading in inequality graphs?
4. How would the graph change if the inequality were \( y > \frac{5}{3}x - 3 \)?
5. What steps would you take to graph \( y \leq \frac{3}{5}x - 1 \)?

**Tip:** Always check the line type (dashed or solid) to decide if the inequality is strict or includes "or equal to."

Which inequality is represented by the graph?

Determine which inequality matches a graph with a line having a slope of 5/3 and y-intercept of -3. Learn how shading and line style indicate inequality signs.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation