Graph Linear Inequalities in Two Variables



2.8 Graph Linear Inequalities in Two Variables

Goal ( Graph linear inequalities in two variables.

Your Notes

VOCABULARY

Linear inequality in two variables

An inequality that can be written in one of the following forms:

Ax + By < C, Ax + By ( C, Ax + By > C, Ax + By ( C

Solution of a linear inequality

An ordered pair (x, y) that makes the inequality true when the values of x and y are substituted into the inequality

Graph of a linear inequality

The set of all points in a coordinate plane that represent solutions of the inequality

Half-plane

The two regions of a coordinate plane that are separated by the boundary line of an inequality

Example 1

Checking solutions of inequalities

Check whether the ordered pairs (a) (3, 2) and (b) ((1, 4) are solutions of

4x + 2y > 6.

|Ordered Pair |Substitute |Conclusion |

|(3, 2) |4( 3 ) + 2( 2 ) |(3, 2) _is_ |

| |= 16 > 6 |a solution. |

|((1, 4) |4( (1 ) + 2( 4 ) |((1, 4) _is not_ |

| |= 4 > 6 |a solution. |

Checkpoint Check whether the ordered pair is a solution of 2x ( y ( 8.

1. (6, 2)

is not a solution

2. (3, (1)

is a solution

Your Notes

GRAPHING A LINEAR INEQUALITY

To graph a linear inequality in two variables, follow these steps:

Step 1 Graph the boundary line for the inequality. Use a _dashed_ line for < or > and a _solid_ line for ( or (.

Step 2 Test a point _not on_ the boundary line to determine whether it is a solution of the inequality. If it _is_ a solution shade the half-plane containing the point. If it _is not_ a solution, shade the other half-plane.

Example 2

Graph a linear inequality with one variable

Graph y < (1 in a coordinate plane.

Solution

1. Graph the boundary line y = (1. Use a _dashed_ line because the inequality symbol is .

2. Test the point (0, 0). Because (0, 0) _is_ a solution of the inequality, shade the portion of the coordinate plane _outside_ the absolute value graph.

Checkpoint Graph the inequality in a coordinate plane.

3. x < (2

4. y ( (x + 2

5. 9x + 3y > 9

6. y ( 2 |x + 2| ( l

Homework

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It is often convenient to use (0, 0) as a test point. However, if (0, 0) lies on a boundary line, you must choose a different test point.

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