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Chapter 7: Problem 10

Graph each linear inequality. \(2 y-x>4\)

Short Answer

Expert verified
The graph of the inequality \(2y - x > 4\) is a dashed line representing the equation \(y =\frac{1}{2}x + 2\), with the region above the line shaded to represent the solution to the inequality.

Step by step solution

01

Convert the Inequality to Slope-Intercept Form

First, rearrange the inequality to the form \(y = mx + b\), where \(m\) represents the slope and \(b\) represents the y-intercept. Begin by shifting \(x\) to the right side of the inequality: \(2y > x + 4\). Then, divide each side by 2 to isolate \(y\): \(y >\frac{1}{2}x + 2\)
02

Draw the Line

Next, graph the boundary line, which corresponds to the equation \(y = \frac{1}{2}x + 2\). Begin at point (0,2) for the y-intercept, and use the slope to find more points. Because the original inequality sign was 'greater than' and not 'greater than or equal to', the line will be dashed to represent that points on the line are not included in the solution.
03

Shading the Area for the Solution

Finally, identify the region of the graph that forms the solution to the inequality. As the inequality is \(y >\frac{1}{2}x + 2\), shade the region above the line to represent all the points where \(y\) is greater than \(\frac{1}{2}x + 2 \)

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What does a dashed line mean in the graph of an inequality?
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