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Chapter 7: Problem 3

Graph each linear inequality. \(3 x-y \geq 6\)

Short Answer

Expert verified
The graph would have the line y=3x-6 as a solid line and the region below this line shaded as that represents the set of all potential solutions to this inequality.

Step by step solution

01

Rewrite in slope-intercept form

First, rearrange the given inequality to the slope-intercept form, \(y = mx + c\). Start by isolating \(y\). Subtract \(3x\) from both sides: \(y \leq 3x - 6\).
02

Graph the line

Next, graph the line as if the inequality is an equation. Start by identifying the y-intercept, which is at \(y = -6\). Then use the slope to find another point. The slope is \(3 = 3/1\), which means for every 1 unit movement to the right on the x-axis, move up 3 units on the y-axis. Plot these points on the graph.
03

Apply the inequality property

Draw a dotted or solid line for the graph. Because the original inequality includes 'equal to' (\(\geq\)), use a solid line. For \(y \leq\), shade everything below the line, because that portion of the plane is the solution region that makes the inequality true.

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Most popular questions from this chapter

Graph each linear inequality. \(y \geq 0\)

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