Question

Graph the inequality on the axes below.
y, is less than or equal to, minus, 2, x, minus, 1
y≤−2x−1

Answer 1

To graph the inequality \( y \leq -2x - 1 \), follow these steps:

1. **Graph the Boundary Line**:
- The inequality \( y = -2x - 1 \) is the boundary line.
- This line has a slope of -2 and a y-intercept of -1.
- Start by plotting the y-intercept (0, -1).
- From there, use the slope to find another point. Since the slope is -2, from (0, -1) move down 2 units and right 1 unit to the point (1, -3). Plot this point as well.
- Draw a solid line through these points to represent that points on this line are included in the inequality (since it is \( \leq \), not \( < \)).

2. **Shade the Appropriate Region**:
- Since the inequality is \( y \leq -2x - 1 \), you will shade the area **below** the line. This indicates that all the points in this region satisfy the inequality.

3. **Label the Axes**: Optionally, label your axes to indicate which direction is positive.

### Summary:
- Draw a solid line for \( y = -2x - 1 \).
- Shade below the line to indicate \( y \leq -2x - 1 \).

This representation will show all the points (x,y) that satisfy the inequality.