Question

Graph the inequality on the axes below.
y, is greater than, minus, start fraction, 2, divided by, 3, end fraction, x, plus, 5
y>−
3
2
​
x+5

Answer 1

To graph the inequality \( y > -\frac{2}{3}x + 5 \), follow these steps:

1. **Graph the line \( y = -\frac{2}{3}x + 5 \)**:
- This is the boundary line of the inequality. To graph this line, you can find two points:
- **Y-intercept**: Set \( x = 0 \):
\[
y = -\frac{2}{3}(0) + 5 = 5
\]
So, the point is \( (0, 5) \).

- **X-intercept**: Set \( y = 0 \):
\[
0 = -\frac{2}{3}x + 5 \quad \Rightarrow \quad \frac{2}{3}x = 5 \quad \Rightarrow \quad x = \frac{5 \cdot 3}{2} = \frac{15}{2} = 7.5
\]
So, the point is \( (7.5, 0) \).

2. **Draw the line**:
- Since the inequality is \( y > \), we draw a **dashed line** for the boundary line \( y = -\frac{2}{3}x + 5 \). The dashed line indicates that the points on the line are not included in the solution.

3. **Shade the region**:
- Since we want the region where \( y \) is greater than the line, shade the area **above the line**. This represents all the points where the \( y \)-value is greater than \( -\frac{2}{3}x + 5 \).

4. **Label the graph**: If you're presenting this graph, make sure to label the x-axis and y-axis, as well as any important points (such as the intercepts).

Now you should have a graph that correctly represents the inequality \( y > -\frac{2}{3}x + 5 \).