Let's start with rewriting this in the form of either y \leq mx + b or y \geq mx + b .

If we end up with y \geq mx + b then we know that all possible solutions for this inequality lie above the line y = mx + b and we shade the region above the line. Why? Because in the region the values of y should be such that are greater than mx + b . Note that all points on the line have values of y that are equal to mx + b . And if you are looking for greater values, you have to go up.

Similarly, if we end up with y \leq mx + b then we know that all possible solution for this inequality lie below the line y = mx + b and we have to shade the region below the line.

Now the question arises whether the line should be dotted or solid. Dotted line means that the line itself is not part of the solution and solid line means it is part of the solution.

Let's take 2x - y \gt -3 .

Subtract 2x from both sides we get

-y \gt -2x - 3

Dividing both sides by -1 , we get

y \lt 2x + 3 .

Since y = 2x + 3 does not satisfy the inequality, the line should be dotted and you should shade the region below the line.

If we take 2x - y \geq - 3 , then this is almost exactly like 2x -y \gt -3 except that the line is solid rather than dotted.

I hope this helps!