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The inequality given is \( y > 1 - 3x \). To graph this, let's break it down:

1. **Rewrite the inequality in slope-intercept form**: The inequality is already in slope-intercept form \( y > mx + b \), where \( m = -3 \) is the slope and \( b = 1 \) is the y-intercept.

2. **Graph the boundary line**: The boundary line is \( y = 1 - 3x \). This is a straight line with slope \( -3 \) and y-intercept \( 1 \). Since the inequality is "greater than" (\( > \)) and not "greater than or equal to," the line will be dashed, indicating that points on the line are *not* included in the solution.

   - Start by plotting the point \( (0, 1) \) (the y-intercept).
   - From there, use the slope \( -3 \) (which means for every 1 unit you move to the right, move 3 units down) to plot additional points.

3. **Determine the shading region**: The inequality \( y > 1 - 3x \) suggests that we shade above the line. This is because the values of \( y \) should be greater than those on the line.

### Identifying the Correct Graph:
- Look for a dashed line with a slope of \( -3 \) (steep downward line).
- The shaded region should be **above** the line.

From the image, the correct graph is the **bottom right** option. It shows a dashed line with a negative slope, and the region above the line is shaded.

Would you like more details or further clarification? Here are 5 related questions to explore this concept further:

1. How would the graph change if the inequality was \( y \geq 1 - 3x \)?
2. How can you tell if a graph represents a strict inequality or an inclusive one?
3. What role does the slope play in determining the steepness of the line?
4. How do you determine which side of the line to shade for inequalities like this?
5. What happens if the inequality is reversed, for example, \( y < 1 - 3x \)?

**Tip**: Always check if the inequality includes the boundary line (solid) or not (dashed).

Learn how to graph the linear inequality y > 1 - 3x. This guide explains how to identify the slope, y-intercept, plot the boundary line, and determine the shaded region for the solution. Suitable for Grades 8-10.

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