Question

this is the graph of a linear inequality. write the inequality in slope-intercept form.
write your answer with y first, followed by an inequality symbol. use integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Identify y-intercept

The line crosses the y-axis at $(0, -2)$, so $b = -2$.

Step2: Calculate slope

Use points $(8, 0)$ and $(0, -2)$:
$$m = \frac{0 - (-2)}{8 - 0} = \frac{2}{8} = \frac{1}{4}$$

Step3: Determine inequality symbol

The line is solid, and the shaded region is above the line, so use $\geq$.

Step4: Write slope-intercept inequality

Substitute $m$ and $b$ into $y \geq mx + b$.

Answer:

$y \geq \frac{1}{4}x - 2$