Question

Determine whether the origin is included in the shaded region and whether the shaded region is above or below the line for the graph of the following inequality: y < 3/2x + 2
The origin is not included in the shaded region and the shaded area is above the line.

The origin is not included in the shaded region and the shaded area is below the line.

The origin is included in the shaded region and the shaded area is above the line.

The origin is included in the shaded region and the shaded area is below the line.

Answer 1

I'll do a similar problem, and I challenge you to do this on your own using similar strategies!

Take y > 7x+2
Plugging in the origin, we have (0,0) as our points, and 0 > 0*7+2=2, so 0>2. As 0 is not greater than 2 (less than is the way that it's pointing), this is false. In addition, as it is y greater than 7x+2, the shaded area is above the line due to that y is greater than, and since y is up and down, greater than means higher than.

Good luck, and feel free to ask any questions that come up!