Question

graph the inequality.
4x - y < -4

Explanation:

Step1: Rewrite the inequality

First, we rewrite the inequality \(4x - y < -4\) in slope - intercept form (\(y=mx + b\)) by solving for \(y\).
Subtract \(4x\) from both sides: \(-y<-4x - 4\).
Multiply both sides by \(- 1\) (and remember to reverse the inequality sign): \(y>4x + 4\).

Step2: Graph the boundary line

The boundary line is \(y = 4x+4\). Since the inequality is \(y>4x + 4\) (not \(y\geq4x + 4\)), the boundary line should be a dashed line.
To graph \(y = 4x + 4\), we can find two points on the line.

• When \(x = 0\), \(y=4(0)+4=4\), so the point \((0,4)\) is on the line.
• When \(x=- 1\), \(y=4(-1)+4 = 0\), so the point \((-1,0)\) is on the line.

Plot these two points and draw a dashed line through them.

Step3: Shade the region

We need to shade the region where \(y>4x + 4\). To determine which side to shade, we can test a point not on the line. Let's use the point \((0,0)\).
Substitute \(x = 0\) and \(y = 0\) into the inequality \(y>4x + 4\): \(0>4(0)+4\) which simplifies to \(0 > 4\), which is false. So we shade the side of the line that does not contain the point \((0,0)\).

Answer:

The graph of the inequality \(4x - y<-4\) (or \(y>4x + 4\)) has a dashed line passing through \((0,4)\) and \((-1,0)\) with the region above the line shaded.