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Depdendent Variable

Number of equations to solve:

Equ. #1:

Equ. #2:

Equ. #3:

Equ. #4:

Equ. #5:

Equ. #6:

Equ. #7:

Equ. #8:

Equ. #9:

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Enter inequality to solve, e.g. 2x+3>4

Enter inequality to graph, e.g. y<3x^2-1

Dependent Variable

Number of inequalities to solve:

Ineq. #1:

Ineq. #2:

Ineq. #3:

Ineq. #4:

Ineq. #5:

Ineq. #6:

Ineq. #7:

Ineq. #8:

Ineq. #9:

Solve for:

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Graphing Linear Inequalities

Questions

1. Graph the region described by y > 2 − 3x.

2. Graph the region described by 2x − y ≥ 3.

3. Graph the region described by

4. Graph the region described by 3x + 4y − 8 ≤ 0.

Solutions

1. First, sketch y = 2−3x, and draw as a dashed line since
we don’t have the equality in the inequality.

You can sketch this using techniques from previous sections
(slope and y-intercept, or getting two points).

Test Point: (0, 0), colored red in diagram below.

y > 2 − 3x
(0) > 2 − 3(0)
0 > 2 FALSE, so shade side opposite the test point.

2. First, sketch 2x − y = 3, and draw as a solid line since
we have the equality in the inequality.

Test Point: (0, 0), colored red in diagram below.

x − y ≥ 3
2(0) − (0) ≥ 3
0 > 3 FALSE, so shade side opposite the test point.

3. First, sketch and draw as a dashed line since
we do not have the equality in the inequality.

Test Point: (−1,−1), colored red in diagram below.

TRUE, so shade side with the test point.

4. First, sketch 3x + 4y − 8 = 0, and draw as a solid line
since we have the equality in the inequality.

Test Point: (0, 0), colored red in diagram below.

3x + 4y − 8 ≤ 0
3(0) + 4(0) − 8 ≤ 0
−8 ≤ TRUE, so shade side with the test point.

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