Answer:
See image
Step-by-step explanation:
To graph a linear equation, the given equation must be in y = mx + b form, or slope-intercept form. Since this inequality is not in slope-intercept form, let's change it to that.
-3x + 2y > -8
Adding 3x to both sides, the inequality becomes 2y > 3x - 8.
Dividing both sides by 2, the inequality becomes y > 3/2x - 4, which is in y = mx + b form.
Now, we need to find a minimum of 2 points to be able to graph. To find two points, plug in values for x to get values of y.
First, plug in 0.
y > 3/2(0) - 4
Evaluating 3/2(0), the inequality becomes y > -4. Therefore, the first point is (0, -4).
Now, plug in 2.
y > 3/2(2) - 4
Evaluating 3/2(2), the inequality becomes y > 3 - 4.
Evaluating 3 - 4, the inequality becomes y > -1. Therefore, the second point is (2, -1).
Now that you have two points, we must graph the line. We can tell whether the line will be solid or dashed by looking at the inequality sign. Since it is ">", or greater than (as opposed to greater than or equal to/less than or equal to), the line will be dashed.
We can tel whether the shading will be on the top of the line or on the bottom of the line by also looking at the sign. Since it is ">" (as opposed to less than/less than or equal to), the shading will be at the top.
Therefore, your graph should look like the attached image.
