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 \((0, 2)\) and \((-5, 0)\). The slope \(m\) is calculated as \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 2}{-5 - 0}=\frac{-2}{-5}=\frac{2}{5}\).

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 \(y=\frac{2}{5}x+2\).

Step3: Determine the inequality symbol

The line is dashed, which means the inequality is either \(y>\frac{2}{5}x + 2\) or \(y<\frac{2}{5}x+2\). We test a point in the shaded region. Let's take the point \((0,3)\) (which is in the shaded region). Substitute \(x = 0\) and \(y = 3\) into the line equation: \(3=\frac{2}{5}(0)+2=2\) is false, but \(3>\frac{2}{5}(0)+2 = 2\) is true. So the inequality is \(y>\frac{2}{5}x+2\).

Answer:

\(y>\frac{2}{5}x + 2\)