Question

find the inequality represented by the graph.

Explanation:

Step1: Identify two points on the line

The two points on the dashed line are \((-3, 0)\) and \((3, -2)\) (assuming the second point is \((3, -2)\) from the graph).

Step2: Calculate the slope (\(m\))

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting the points \((x_1,y_1)=(-3,0)\) and \((x_2,y_2)=(3,-2)\), we get \(m=\frac{-2 - 0}{3 - (-3)}=\frac{-2}{6}=-\frac{1}{3}\).

Step3: Find the equation of the line

Using the point - slope form \(y - y_1=m(x - x_1)\) with \((x_1,y_1)=(-3,0)\) and \(m =-\frac{1}{3}\), we have:
\(y-0=-\frac{1}{3}(x + 3)\)
\(y=-\frac{1}{3}x-1\)

Step4: Determine the inequality

Since the line is dashed, the inequality is either \(y>-\frac{1}{3}x - 1\) or \(y<-\frac{1}{3}x - 1\). We test a point in the shaded region, say \((0,0)\). Substituting into \(y\) and \(-\frac{1}{3}x - 1\), we get \(0\) and \(- 1\). Since \(0>-1\), the inequality is \(y>-\frac{1}{3}x - 1\).

Answer:

\(y>-\frac{1}{3}x - 1\)