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 line intercepts

The line crosses the y-axis at $(0, 5)$ and the x-axis at $(5, 0)$.

Step2: Calculate slope

Slope $m = \frac{y_2-y_1}{x_2-x_1} = \frac{0-5}{5-0} = -1$

Step3: Write line equation

Using slope-intercept $y=mx+b$, $b=5$, so $y = -x + 5$.

Step4: Determine inequality symbol

Shaded area is below the solid line, so use $\leq$.

Answer:

$y \leq -x + 5$