Question

this is the graph of a linear inequality. write the inequality in slope - intercept form.
write your answer with y first, followed by an inequality symbol. use integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Find the slope of the line

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

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 \(y=\frac{1}{2}x+2\).

Step3: Determine the inequality symbol

The shaded region is above the line, and the line is solid (so the inequality includes equality). So the inequality symbol is \(\geq\).

Answer:

\(y\geq\frac{1}{2}x + 2\)