Question

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

Explanation:

Step1: Find the slope of the line

The line passes through \((0, -2)\) and \((4, -4)\). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-4 - (-2)}{4 - 0}=\frac{-2}{4}=-\frac{1}{2}\).

Step2: Determine the y - intercept

The line crosses the y - axis at \((0, -2)\), so \(b=-2\). The equation of the line in slope - intercept form (\(y = mx + b\)) is \(y=-\frac{1}{2}x - 2\).

Step3: Determine the inequality symbol

The line is dashed, so the inequality is either \(y<-\frac{1}{2}x - 2\) or \(y>-\frac{1}{2}x - 2\). The shaded region is below the line, so we use the less - than symbol.

Answer:

\(y<-\frac{1}{2}x - 2\)