Question

c. shade the region that represents the solution set to the inequality 2y - x > 1.

Explanation:

Step1: Rewrite the inequality

First, rewrite \(2y - x>1\) as \(y>\frac{1}{2}x+\frac{1}{2}\).

Step2: Identify the boundary - line

The boundary - line of the inequality \(y>\frac{1}{2}x+\frac{1}{2}\) is the equation \(y = \frac{1}{2}x+\frac{1}{2}\), which is a straight line with slope \(m=\frac{1}{2}\) and \(y\) - intercept \(b = \frac{1}{2}\).

Step3: Determine the shading region

Since the inequality is \(y>\frac{1}{2}x+\frac{1}{2}\) (a strict inequality), we will draw a dashed line for \(y=\frac{1}{2}x+\frac{1}{2}\). To find which side of the line to shade, we can test a point. Let's test the point \((0,0)\). Substitute \(x = 0\) and \(y = 0\) into the inequality: \(0>\frac{1}{2}(0)+\frac{1}{2}\), or \(0>\frac{1}{2}\), which is false. So, we shade the region that does not contain the point \((0,0)\), which is the region above the line \(y=\frac{1}{2}x+\frac{1}{2}\).

Answer:

Shade the region above the dashed line \(y=\frac{1}{2}x+\frac{1}{2}\).