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Which inequality has the graph shown below?

The graph shows a region shaded on the left side of a dashed line, indicating that the inequality does not include the boundary (since the line is dashed). The line has a positive slope and passes through the origin (0,0), which suggests it is of the form:

\[
y = mx
\]

The slope \( m \) is calculated by finding the change in \( y \) divided by the change in \( x \). From the graph, for each unit the line moves right by 1, it moves up by 1, giving a slope \( m = 1 \). So, the equation of the line is:

\[
y = x
\]

Now, because the region is shaded to the left of the line, we are considering points where the \( y \)-value is less than \( x \), but the line is not included (dashed line). Therefore, the inequality is:

\[
y < x
\]

Thus, the inequality represented by the graph is:

\[
y < x
\]

Would you like further details or have any questions?

Here are five related questions for further exploration:
1. How would the graph change if the inequality was \( y \leq x \)?
2. What is the effect of changing the slope of the line in an inequality like \( y < 2x \)?
3. How do you determine the shading for a quadratic inequality, such as \( y > x^2 \)?
4. What is the relationship between the inequality sign and the type of line (solid or dashed)?
5. How would the inequality look if the shaded region was above the line instead?

**Tip:** Always test a point from the shaded region (e.g., \( (-1, -2) \)) to verify whether it satisfies the inequality.

Analyze the graph of the inequality y < x. Learn how the shaded region, dashed boundary, and positive slope indicate the inequality. Suitable for students in Grades 8-10.

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