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 \((0, -2)\) 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 y - intercept \(b\) is the value of \(y\) when \(x = 0\). From the point \((0, -2)\), we know that \(b=-2\). So 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 line is a solid line (since the boundary is included in the solution set) and the shaded region is above the line. So the inequality symbol is \(\geq\).

Answer:

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