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: Find slope of boundary line

Identify two points on the line: $(0,3)$ and $(3,0)$. Slope $m=\frac{0-3}{3-0}=-1$.

Step2: Write line equation (slope-intercept)

Slope-intercept form is $y=mx+b$. $b=3$ (y-intercept), so $y=-x+3$.

Step3: Determine inequality symbol

Boundary is dashed, shaded area is above the line, so use $>$.

Step4: Final inequality form

Combine to get the slope-intercept inequality.

Answer:

$y > -x + 3$