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

Step2: Determine the equation of the line

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. Here, \(m=\frac{3}{2}\) and \(b = 3\), so the equation of the line is \(y=\frac{3}{2}x + 3\).

Step3: Determine the inequality symbol

The line is solid (since the boundary is included in the solution set) and the shaded region is above the line. So the inequality symbol is \(\geq\).

Answer:

\(y\geq\frac{3}{2}x + 3\)