**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.