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 slope and intercept

The line crosses the y-axis at $(0,5)$, so $b=5$. Using points $(0,5)$ and $(5,0)$, slope $m=\frac{0-5}{5-0}=-1$.

Step2: Write line equation

Slope-intercept form: $y = mx + b$
$y = -x + 5$

Step3: Determine inequality symbol

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

Answer:

$y \geq -x + 5$