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. And the grid is only 10 by 10 by -10 by -10.
y>−3x−8

Answer 1

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

1. **Identify the boundary line**: The corresponding equation is \( y = -3x - 8 \). This line will be dashed because the inequality is "greater than" (>) and does not include equality.

2. **Find the y-intercept and slope**:
- The y-intercept occurs when \( x = 0 \):
\[
y = -3(0) - 8 = -8
\]
So the y-intercept is (0, -8).

- The slope is -3, meaning for every 1 unit increase in \( x \), \( y \) decreases by 3 units.

3. **Find another point on the line**:
- Choose \( x = 1 \):
\[
y = -3(1) - 8 = -11
\]
So another point is (1, -11). But this point is outside of our grid, so let's try \( x = -2 \):
\[
y = -3(-2) - 8 = 6 - 8 = -2
\]
So the point (-2, -2) lies on the line.

4. **Plotting the points**:
- Plot the points (0, -8) and (-2, -2).
- Draw a dashed line through these points because it corresponds to a "greater than" inequality.

5. **Shading the region**:
- Since we want points where \( y \) is greater than \( -3x - 8 \), we will shade above the line.

### Summary:
- **Boundary line**: Dashed
- **Points used**: (0, -8) and (-2, -2)
- **Shading**: Above the dashed line

### Points:
Thus, the points for your graph are:
1. (0, -8)
2. (-2, -2)

The shaded area will be above the dashed line you drew for the inequality \( y > -3x - 8 \).