Question

Graph the inequality on the axes below.
y, is less than, start fraction, 3, divided by, 5, end fraction, x, plus, 2
y<
5
3
​
x+2

Answer 1

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

1. **Graph the boundary line:** First, graph the equation \( y = \frac{3}{5}x + 2 \). This line is the boundary for the inequality.
- The slope is \( \frac{3}{5} \), which means for every 5 units you move to the right (positive x-direction), you move up 3 units (positive y-direction).
- The y-intercept is \( 2 \), meaning the line crosses the y-axis at the point (0, 2).
- To find another point, you can choose a value for \( x \) (e.g., \( x = 5 \)):
\[
y = \frac{3}{5}(5) + 2 = 3 + 2 = 5
\]
So the point (5, 5) is also on the line.

Now you can plot the points (0, 2) and (5, 5) and draw a **dashed line** between them. The line should be dashed because the inequality is strict (it's "<" not "≤"), indicating that points on the line are not included in the solution set.

2. **Shading the region:** Since the inequality is \( y < \frac{3}{5}x + 2 \), shade the region below the line. This represents all the points where the y-value is less than the value given by the line.

3. **Labeling the axes:** Make sure to label your x-axis and y-axis for clarity.

### Summary of the Graph:
- Dashed line for \( y = \frac{3}{5}x + 2 \).
- Shade below the line to indicate \( y < \frac{3}{5}x + 2 \).

### Note:
If you are plotting this on graph paper or a digital graphing tool, ensure to choose an appropriate scale for both axes to accurately represent the line and shading.