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How do you know if you need to shade above or below the line?

Answer 1

Eva Adamson

The direction of the inequality will tell you this information.

Example: #y >= 2x+3#

You would draw the line #y = 2x+3# and shade above the line, since #y# is also greater than # 2x+3#.

graph{y>=2x+3 [-10, 10, -5, 5]}

Example: #y < 1/2x-2#

You would draw the line #y=1/2x-2# as a dashed line, then shade below the line since #y# is less than #1/2x-2#.

graph{y<1/2x-2 [-10, 10, -5, 5]}

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Answer 2

Savannah Anderson

To determine whether to shade above or below the line when graphing an inequality, follow these steps:

Substitute a test point into the original inequality that is not on the line.
If the inequality is true when the test point is substituted, shade the region where the test point lies. If it is false, shade the opposite region.
The shaded region represents the solution to the inequality.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.