this is the graph of a linear inequality. write the inequality in slope-intercept form.

Answer:

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

Explanation:

Step1: Find the slope of the line

The line passes through $(0, 6)$ and $(4, 0)$. The slope $m$ is calculated as $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 6}{4 - 0}=\frac{-6}{4}=-\frac{3}{2}$.

Step2: Determine the equation of the line

Using the slope - intercept form $y = mx + b$, where $b = 6$ (the y - intercept) and $m=-\frac{3}{2}$, the equation of the line is $y=-\frac{3}{2}x + 6$.

Step3: Determine the inequality symbol

The line is solid (so the inequality is either $\geq$ or $\leq$) and the shaded region is above the line. For a linear inequality in slope - intercept form $y=mx + b$, if the shaded region is above the line, the inequality is $y\geq mx + b$. So the inequality is $y\geq-\frac{3}{2}x + 6$.