Question

$y > -\frac{6}{5}x + 2$
plot points on the boundary line. select the line to switch between solid and dotted. select a region to shade it.

Explanation:

Step1: Identify the boundary line equation

The inequality is \( y > -\frac{6}{5}x + 2 \). The boundary line is \( y = -\frac{6}{5}x + 2 \) (dotted line since the inequality is strict, \( > \), not \( \geq \)).

Step2: Find two points on the boundary line

• When \( x = 0 \): \( y = -\frac{6}{5}(0) + 2 = 2 \). So the point is \( (0, 2) \).
• When \( x = 5 \): \( y = -\frac{6}{5}(5) + 2 = -6 + 2 = -4 \). So the point is \( (5, -4) \).

Step3: Determine the shading region

Since the inequality is \( y > -\frac{6}{5}x + 2 \), we shade the region above the boundary line. We can test a point not on the line, e.g., \( (0, 3) \). Plugging into the inequality: \( 3 > -\frac{6}{5}(0) + 2 \) → \( 3 > 2 \), which is true. So we shade above the dotted line passing through \( (0, 2) \) and \( (5, -4) \).

Answer:

1. Plot the boundary line (dotted) through points \((0, 2)\) and \((5, -4)\).
2. Shade the region above this dotted line.