Question

Graph the inequality on the axes below.
y, is greater than or equal to, minus, one half, x, plus, 7
y≥−
2
1
​
x+7

Answer 1

To graph the inequality \( y \geq -\frac{1}{2}x + 7 \), follow these steps:

1. **Graph the boundary line**: First, graph the equation \( y = -\frac{1}{2}x + 7 \).
- This line has a y-intercept of 7 (point (0, 7)).
- The slope is -1/2, which means for every 2 units you move to the right (positive x direction), you move 1 unit down (negative y direction).

**To plot two points:**
- Start with the y-intercept: (0, 7).
- Use the slope: From (0, 7), if you move 2 to the right (to x = 2), you go down 1 (to y = 6), giving you the point (2, 6).

2. **Draw a dashed or solid line**: Since the inequality is \( \geq \), we use a solid line to indicate that points on the line are included in the solution set.

3. **Shade the region**: Since the inequality is \( y \geq -\frac{1}{2}x + 7 \), shade the region above the line, as this represents all the points where \( y \) is greater than or equal to the line.

Your graph should look something like this:

```
y
↑
|
| •(0,7)
| •
| •
| •
| •
| •
| •
|__________________________________→ x
```

With the line drawn and the region above the line shaded.