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 the slope-intercept form of the line

The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. From the graph, the line passes through the points $(0, -3)$ (y-intercept, so $b = -3$) and $(3, 0)$. The slope $m$ is calculated as $\frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-3)}{3 - 0} = \frac{3}{3} = 1$. So the equation of the line is $y = x - 3$.

Step2: Determine the inequality symbol

The line is solid (so the inequality includes equality) and the shaded region is above the line (so we use $\geq$ or $\leq$; since above, for $y$, it's greater). So the inequality is $y \geq x - 3$.

Answer:

$y \geq x - 3$