Question

this is the graph of a linear inequality. write the inequality in slope - intercept form.

Explanation:

Step1: Find the slope and y-intercept of the line

The line passes through the points \((0, 4)\) (y-intercept) and \((4, 0)\). The slope \(m\) is calculated as \(\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 4}{4 - 0}=\frac{-4}{4}=-1\). The equation of the line in slope - intercept form \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept) is \(y=-x + 4\).

Step2: Determine the inequality symbol

The line is dashed, so the inequality is either \(y>-x + 4\) or \(y<-x + 4\). We test a point in the shaded region, for example, \((0,5)\). Substitute \(x = 0\) and \(y = 5\) into \(y=-x + 4\), we get \(5>-0 + 4\) (i.e., \(5 > 4\)) which is true. So the inequality is \(y>-x + 4\).

Answer:

\(y > -x + 4\)