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When graphing a linear inequality, we generally follow these steps:
Endpoint IS included in interval | Endpoint IS NOT included in interval |
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< or > |
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EXAMPLE
Graph the linear inequalityStep | Explanation | Graph |
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1. Use solid or dashed line. | To start, we note that the inequality symbol is strict, thus we will use a dashed line. |
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2. Graph the equation of the line as ![]() |
Next, we note the y-intercept of -5 and the positive slope of 2 to create the start of our graph. |
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3. Shade above or below the line. |
Since our inequality is ![]() |
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Results Driven: Skill in Action |
While using the above method to determine which half of the coordinate plane to shade, there is a more mathematically sound method. This method will be particularly useful when graphing non-linear inequalities, where "above the line" and "below the line" aren't as clear cut.
A test point is any coordinate (x, y) that does not lie on the boundary line. We can think of it as being a representative for all other coordinates on that side of the boundary line. If our test point satisfies the inequality, it represents a solution, as do all the other points on that side. If our test point does not satisfy the inequality, then it represents a non-solution, and the other side of the boundary line should be shaded.
EXAMPLE
Consider the example from above. Suppose we have completed Step 2 and have drawn our boundary line. Now we need to determine which side to shade.
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Our inequality |
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Use (0, 0) as our test point. |
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Evaluate 2(0). |
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Evaluate ![]() ![]() |
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