Question

What is the graph of the inequality?

3x + 2y > –5

Answer 1

To graph the inequality 3x + 2y > -5, we first need to rewrite it in slope-intercept form, which is y > mx + b.

To do this, we isolate y on one side of the inequality:
3x + 2y > -5
2y > -3x - 5
y > (-3/2)x - 5/2

Now we can graph this inequality as a dotted line with a slope of -3/2 and a y-intercept of -5/2. Since this is a "greater than" inequality, the line will be dotted to indicate that points on the line are not included in the solution.

Next, we need to determine which side of the line to shade in. We can select a test point that is not on the line such as (0, 0) and substitute its x and y values into the inequality:

3(0) + 2(0) > -5
0 > -5

Since the inequality is true, we shade the side of the line that contains the test point. In this case, we shade the region above the line.

Therefore, the graph of the inequality y > (-3/2)x - 5/2 is a dotted line with a slope of -3/2 and a y-intercept of -5/2, and the region above the line is shaded.