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

Step2: Determine the y-intercept

The y-intercept \(b\) is the value of \(y\) when \(x = 0\). From the point \((0, -2)\), we get \(b=-2\).

Step3: Write the equation of the line

The slope - intercept form of a line is \(y = mx + b\). Substituting \(m=\frac{1}{4}\) and \(b = - 2\), we get \(y=\frac{1}{4}x-2\).

Step4: Determine the inequality symbol

The line is dashed, which means the inequality is either \(y>\frac{1}{4}x - 2\) or \(y<\frac{1}{4}x - 2\). The shaded region is above the line, so we use the greater - than symbol.

Answer:

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