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 $(0, 6)$ and $(4, 0)$. The slope $m$ is calculated as $\frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 6}{4 - 0} = \frac{-6}{4} = -\frac{3}{2}$. The y-intercept $b$ is 6 (since the line crosses the y-axis at $(0, 6)$). So the equation of the line is $y = -\frac{3}{2}x + 6$.

Step2: Determine the inequality symbol

The shaded region is above the line, and the line is solid (since the boundary is included in the solution set). So the inequality symbol is $\geq$.

Answer:

$y \geq -\frac{3}{2}x + 6$