Which is the graph of the linear inequality y < 3x + 1?

On a coordinate plane, a solid straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything to the left of the line is shaded.
On a coordinate plane, a solid straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything to the right of the line is shaded.
On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything to the left of the line is shaded.
On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything to the right of the line is shaded.

The correct graph for the linear inequality \( y < 3x + 1 \) is:

**On a coordinate plane, a dashed straight line has a positive slope and goes through (-1, -2) and (0, 1). Everything to the left of the line is shaded.**

Here's why:
- **Dashed Line:** The line is dashed because the inequality is strict ("<") and does not include the line itself.
- **Positive Slope:** The line has a positive slope (slope = 3).
- **Shading:** Since \( y \) is less than \( 3x + 1 \), the region below the line (or to the left when you consider the orientation of the graph) is shaded.

Would you like more details or have any questions?

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Here are five related questions:
1. How would the graph change if the inequality were \( y \leq 3x + 1 \)?
2. What would the graph look like for the inequality \( y > 3x + 1 \)?
3. How do you determine which side of the line to shade for a given inequality?
4. What is the significance of the slope in the equation \( y = 3x + 1 \)?
5. How does changing the y-intercept affect the graph of the inequality?

**Tip:** When graphing inequalities, always use a dashed line for strict inequalities (like "<" or ">") and a solid line for inclusive inequalities (like "≤" or "≥").

Learn how to graph the linear inequality y < 3x + 1 on a coordinate plane. Understand why a dashed line with a positive slope is used, passing through (-1, -2) and (0, 1), with shading to the left of the line. Suitable for students in Grades 7-9.

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