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 points \((0, 1)\) and \((1, -3)\) (we can identify these from the graph). The slope \(m\) is calculated as \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-3 - 1}{1 - 0}=\frac{-4}{1}=-4\).

Step2: Determine the y - intercept

The line crosses the y - axis at \((0, 1)\), so the y - intercept \(b = 1\). The equation of the line in slope - intercept form (\(y=mx + b\)) is \(y=-4x + 1\).

Step3: Determine the inequality symbol

The line is dashed, which means the inequality is either \(y>-4x + 1\) or \(y<-4x + 1\). The shaded region is to the right of the dashed line. We can test a point in the shaded region, for example, \((0, 2)\). Substitute \(x = 0\) and \(y = 2\) into the inequality. If we use \(y>-4x + 1\), when \(x = 0\), \(y>1\), and \(2>1\) is true. So the inequality is \(y>-4x + 1\).

Answer:

\(y > - 4x+1\)