Question

Graph the inequality on the axes below.
3, x, plus, y, is greater than, minus, 7
3x+y>−7
x
y
x
y

Answer 1

To graph the inequality \(3x + y > -7\), we will first graph the related equation, which is \(3x + y = -7\), and then shade the appropriate region.

### Step 1: Graph the boundary line
1. **Finding the intercepts**:
- **x-intercept**: Set \(y = 0\):
\[
3x + 0 = -7 \implies 3x = -7 \implies x = -\frac{7}{3} \approx -2.33
\]
So the x-intercept is \((-2.33, 0)\).
- **y-intercept**: Set \(x = 0\):
\[
3(0) + y = -7 \implies y = -7
\]
So the y-intercept is \((0, -7)\).

2. **Plotting points**: Plot the points \((-2.33, 0)\) and \((0, -7)\) on the graph.

3. **Drawing the line**: Since the inequality is \(>\) (not \(\geq\)), we will draw a dashed line through these points to indicate that points on the line are not included in the solution set.

### Step 2: Shading the appropriate region
To determine which side of the line to shade, we can select a test point not on the line, such as \((0, 0)\):
\[
3(0) + 0 > -7 \implies 0 > -7
\]
This statement is true, indicating that the region containing the point \((0, 0)\) is part of the solution. Therefore, we shade the region above the line \(3x + y = -7\).

### Summary
- The boundary line \(3x + y = -7\) is dashed.
- The region above the line is shaded, representing the solution to the inequality \(3x + y > -7\).

### Graph Representation
If you would like a visual representation, you would typically use graphing software, but here's a simple representation of the description above:

```plaintext
y
|
| * (0, -7)
| \
| \
| \
| \ shaded region (above the line)
| \
| \
---|---------------*---------------- x
| (-2.33, 0)
|
|
```

In a actual graphing utility, please utilize the steps I provided to accurately represent the inequality.