Question

#3 - which of the graphs below matches the following inequality? *
17 points
$y>-x - 5$
rectangle
rhombus
pentagon
quadrilateral

Explanation:

Step1: Analyze the boundary line

The inequality is \(y > -x - 5\). The boundary line is \(y=-x - 5\). The slope \(m=- 1\) and the \(y\) - intercept \(b =-5\). Since the inequality is \(y> -x - 5\) (not \(y\geq -x - 5\)), the boundary line is dashed.

Step2: Test a point

Let's test the point \((0,0)\). Substitute \(x = 0\) and \(y = 0\) into the inequality \(y> -x - 5\). We get \(0>-(0)-5\), which simplifies to \(0>-5\) (a True statement). So, the region containing the point \((0,0)\) is the solution region.

Answer:

The fourth graph (quadrilateral - shaped graph with the dashed line \(y=-x - 5\) and the region above the line shaded) is the correct graph for the inequality \(y >-x - 5\).