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

Step2: Determine the y - intercept

The line crosses the y - axis at \((0, 4)\), so the y - intercept \(b = 4\). The equation of the line in slope - intercept form (\(y=mx + b\)) is \(y=\frac{4}{3}x + 4\).

Step3: Determine the inequality symbol

The line is dashed, so the inequality is either \(y>\frac{4}{3}x + 4\) or \(y<\frac{4}{3}x + 4\). The shaded region is above the line, so we use the greater - than symbol.

Answer:

\(y>\frac{4}{3}x + 4\)