Question

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

Explanation:

Step1: Find slope from intercepts

The line crosses $(0,6)$ and $(6,0)$. Slope $m=\frac{0-6}{6-0}=-1$.

Step2: Write slope-intercept equation

Using $y=mx+b$, $b=6$, so $y=-x+6$.

Step3: Determine inequality symbol

Shaded area is above line; line is solid, so use $\geq$.

Step4: Final inequality form

Rearrange to $y$ first: $y\geq -x+6$.

Answer:

$y\geq -x+6$