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 the points \((-6, 0)\) and \((0, 2)\). The slope \(m\) is calculated as \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{2 - 0}{0 - (-6)}=\frac{2}{6}=\frac{1}{3}\).

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 \(y=\frac{1}{3}x+2\).

Step3: Determine the inequality symbol

The line is dashed, so the inequality is either \(y>\frac{1}{3}x + 2\) or \(y<\frac{1}{3}x+2\). The shaded region is above the line, so we use the greater - than symbol.

Answer:

\(y>\frac{1}{3}x + 2\)