Questions: Graphing Inequalities Graph the following inequality. Note: To graph the inequality: 1. Select the type of line below (solid or dashed). 2. Plot two points on the line. 3. Click on the side that should be shaded. y < 1/5 x + 2

Graphing Inequalities
Graph the following inequality.
Note: To graph the inequality:
1. Select the type of line below (solid or dashed).
2. Plot two points on the line.
3. Click on the side that should be shaded.
y < 1/5 x + 2

Transcript text: Graphing Inequalities Graph the following inequality. Note: To graph the inequality: 1. Select the type of line below (solid or dashed). 2. Plot two points on the line. 3. Click on the side that should be shaded. \[ y<\frac{1}{5} x+2 \]

Solution

Solution Steps

Step 1: Identify the inequality

The given inequality is \( y \leq \frac{3}{5}x + 2 \).

Step 2: Determine the type of line

Since the inequality is \( \leq \), we will use a solid line to represent the boundary.

Step 3: Plot the boundary line

Find the y-intercept (where \( x = 0 \)): \( y = 2 \).
Find another point using the slope \( \frac{3}{5} \). From the y-intercept (0, 2), move up 3 units and right 5 units to get the point (5, 5).

Step 4: Draw the line

Draw a solid line through the points (0, 2) and (5, 5).

Step 5: Shade the appropriate region

Since the inequality is \( y \leq \frac{3}{5}x + 2 \), shade the region below the line.