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 \((8, 0)\). The slope \(m\) is calculated as \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - (-2)}{8 - 0}=\frac{2}{8}=\frac{1}{4}\).

Step2: Determine the y-intercept

The line crosses the y - axis at \((0, -2)\), so the y - intercept \(b=-2\). The equation of the line in slope - intercept form (\(y = mx + b\)) is \(y=\frac{1}{4}x-2\).

Step3: Determine the inequality symbol

The shaded region is below the line, and the line is solid (since the boundary is included in the solution set), so the inequality is \(y\leq\frac{1}{4}x - 2\).

Answer:

\(y\leq\frac{1}{4}x - 2\)