Question

what inequality is shown by each graph?
see example 3
24.
25.
26.

Explanation:

Step1: Find line eq for Q24

First, identify two points on the line: $(0, -3)$ and $(-2, 0)$.
Slope $m = \frac{0 - (-3)}{-2 - 0} = -\frac{3}{2}$.
Y-intercept $b = -3$, so line equation: $y = -\frac{3}{2}x - 3$.
The line is solid, and the region below is shaded, so inequality: $y \leq -\frac{3}{2}x - 3$.

Step2: Find line eq for Q25

Identify two points on the dashed line: $(-4, -1)$ and $(0, 1)$.
Slope $m = \frac{1 - (-1)}{0 - (-4)} = \frac{2}{4} = \frac{1}{2}$.
Y-intercept $b = 1$, so line equation: $y = \frac{1}{2}x + 1$.
The line is dashed, and the region above is shaded, so inequality: $y > \frac{1}{2}x + 1$.

Answer:

1. $y \leq -\frac{3}{2}x - 3$
2. $y > \frac{1}{2}x + 1$