Question

what inequality is shownsee example 324.25.

Explanation:

Problem 24:

Step1: Find line equation

First, identify two points on the line: $(0, -4)$ and $(-2, 0)$.
Slope $m = \frac{0 - (-4)}{-2 - 0} = \frac{4}{-2} = -2$.
Y-intercept $b = -4$, so line equation: $y = -2x - 4$.

Step2: Determine inequality sign

The line is solid, and the shaded region is above the line. Use $\geq$.
Inequality: $y \geq -2x - 4$ or $2x + y \geq -4$.

Problem 25:

Step1: Find line equation

Identify two points on the line: $(0, 1)$ and $(-5, 0)$.
Slope $m = \frac{0 - 1}{-5 - 0} = \frac{-1}{-5} = \frac{1}{5}$.
Y-intercept $b = 1$, so line equation: $y = \frac{1}{5}x + 1$.

Step2: Determine inequality sign

The line is dashed, and the shaded region is below the line. Use $<$.
Inequality: $y < \frac{1}{5}x + 1$ or $x - 5y > -5$.

Answer:

1. $y \geq -2x - 4$ (or $2x + y \geq -4$)
2. $y < \frac{1}{5}x + 1$ (or $x - 5y > -5$)