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

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 \(y=\frac{2}{3}x-4\).

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 (since when we test a point in the shaded region, say \((0,0)\), substituting into \(y\) and \(\frac{2}{3}x - 4\): \(0\) and \(\frac{2}{3}(0)-4=-4\), and \(0>-4\)). So the inequality is \(y\geq\frac{2}{3}x - 4\).

Answer:

\(y\geq\frac{2}{3}x - 4\)