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 \((0, 0)\) and \((1, -2)\) (we can find another point by looking at the graph). The slope \(m\) is calculated as \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-2 - 0}{1 - 0}=-2\).

Step2: Determine the y - intercept

The line crosses the y - axis at \((0, 0)\), so the y - intercept \(b = 0\). The equation of the line in slope - intercept form \(y=mx + b\) is \(y=-2x+0\) or \(y = - 2x\).

Step3: Determine the inequality symbol

The line is dashed (so the inequality is strict, either \(>\) or \(<\)) and the shaded region is above the line. For a line \(y=mx + b\), if the shaded region is above the line, the inequality is \(y>mx + b\). So substituting \(m=-2\) and \(b = 0\), we get \(y>-2x\).

Answer:

\(y > - 2x\)