Question

Graph the inequality on the axes below. And give both of the ( , ) points. and rather to shade above or below, and dashed or soild line.
y>−3x−8

Answer 1

To graph the inequality \( y > -3x - 8 \), follow these steps:

1. **Identify the boundary line**: The equation \( y = -3x - 8 \) is a linear equation and represents the boundary line of the inequality.

2. **Determine the type of line**: Since the inequality is ">" (greater than) and not "≥" (greater than or equal to), we will use a dashed line for the boundary. This means that points on the line are not included in the solution set.

3. **Find points for the line**: To graph the line, you can find two points by substituting two values for \( x \).

- **Point 1**: Let’s use \( x = 0 \):
\[
y = -3(0) - 8 = -8 \quad \Rightarrow \quad (0, -8)
\]

- **Point 2**: Let’s use \( x = 2 \):
\[
y = -3(2) - 8 = -6 - 8 = -14 \quad \Rightarrow \quad (2, -14)
\]

4. **Plot the points**: Plot the points (0, -8) and (2, -14) on the graph.

5. **Draw the dashed line**: Connect the points with a dashed line to indicate that this line is not included in the solution.

6. **Shade the appropriate region**: The inequality \( y > -3x - 8 \) indicates that we will shade above the line because we are interested in values of \( y \) that are greater than those on the line.

### Summary:

- Points: \((0, -8)\) and \((2, -14)\)
- Line Type: Dashed line
- Shading: Above the line

This graphical representation allows you to understand the solution set of the inequality.