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

Explanation:

Step1: Find two points on the line

Let's take two points on the dashed - line, say $(0, - 3)$ and $(6,-6)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting the points $(x_1,y_1)=(0, - 3)$ and $(x_2,y_2)=(6,-6)$ into the formula, we get $m=\frac{-6-( - 3)}{6 - 0}=\frac{-6 + 3}{6}=\frac{-3}{6}=-\frac{1}{2}$.

Step3: Find the y - intercept $b$

The y - intercept is the y - coordinate of the point where the line crosses the y - axis. From the point $(0,-3)$, we know that $b=-3$.

Step4: Write the equation of the line

The slope - intercept form of a line is $y = mx + b$. So the equation of the line is $y=-\frac{1}{2}x-3$.

Step5: Determine the inequality

Since the line is dashed and the region above the line is shaded, the inequality is $y>-\frac{1}{2}x - 3$.

Answer:

$y>-\frac{1}{2}x - 3$