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Chapter 7: Problem 2

Graph each linear inequality. \(x-y \leq 1\)

Short Answer

Expert verified
The graph of the inequality \(x - y \leq 1\) is a solid line going through the points (0, 1) and (1, 0) with the area above the line shaded.

Step by step solution

01

Rewrite in slope-intercept form

The first thing you want to do is rewrite the equation in slope-intercept form (y = mx + b). The original equation is \(x - y \leq 1\). You isolate y by subtracting x from both sides, which gives \(y \geq -x + 1\).
02

Plot the line

Now, plot the line using the slope and y-intercept, in this case the line is \(y = -x + 1\). After that, the line can be drawn. Since the inequality includes 'equal to', the line will be a solid line because any point on the line also satisfies the inequality.
03

Shade the appropriate area

To finish the graph, decide whether to shade above or below the line. As the inequality is 'greater than or equals', shade above the line. This means, any point in that shaded area makes the inequality true.

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