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Chapter 7: Problem 11

Graph each linear inequality. \(y>\frac{1}{3} x\)

Short Answer

Expert verified
The graph of the inequality \(y > \frac{1}{3} x\) is a dashed line, representing \(y=\frac{1}{3}x\), with the area above this line shaded, indicating all the points that satisfy the given inequality.

Step by step solution

01

Identify the inequality

The given inequality is \(y > \frac{1}{3} x\). This inequality can be graphed on a coordinate plane.
02

Understand the inequality

Since the inequality is \(y>\frac{1}{3}x\), this means that we are looking for all the points (x, y) for which y is greater than \(\frac{1}{3}x\). In other words, we want all the points above the line \(y=\frac{1}{3}x\).
03

Graph the boundary line

First, graph the line \(y=\frac{1}{3}x\). This is a straight line with a slope of 1/3 and passing through the origin (0, 0). Because the inequality sign is strictly 'greater than' and not 'greater than or equal to', the line should be drawn as a dashed line. The dashed line signifies that points on the line are not included in the solution of the inequality.
04

Shading the solution region

Next, to denote the points for which y is greater than \(\frac{1}{3}x\), shade the region above the line. All the points in this shaded region are solutions to the inequality.

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