What's a Half-Plane?

The line of a graphed inequality, also called a boundary, divides the coordinate plane into two halves, or half-planes
If we graph the inequality 'y>2x-2', we can see what a boundary and the two half-planes look like
The line of a graphed inequality will look just like the graphed line 'y=2x-2', but the line will be dashed instead of solid
We shade the region that the inequality 'y>2x-2' represents, which is to the left of the dashed 'y=2x-2' line
The shaded region is the "closed" half-plane, and the unshaded region is the "open" half-plane

1. So the line of a graphed inequality, also called a boundary, divides the coordinate plane into two halves, or half-planes
1. So the line of a graphed inequality, also called a boundary, divides the coordinate plane into two halves, or half-planes
1. 'y>2x-2' is an inequality, so let's graph it to see what a boundary and the two half-planes look like
1. The line of a graphed inequality is also called a boundary
2. The line of a graphed inequality will look just like the graphed line 'y=2x-2', but the line will be dashed instead of solid
1. So the line of a graphed inequality, also called a boundary, divides the coordinate plane into two halves, or half-planes
1. We want to shade the region that the inequality 'y>2x-2' represents
1. We want to shade the region that the inequality 'y>2x-2' represents, which is to the left of the dashed 'y=2x-2' line
1. We want to shade the region that the inequality 'y>2x-2' represents, which is to the left of the dashed 'y=2x-2' line
1. We want to shade the region that the inequality 'y>2x-2' represents, which is to the left of the dashed 'y=2x-2' line
2. The unshaded region to the right of the boundary is called the "open" half-plane
1. So the line of a graphed inequality, also called a boundary, divides the coordinate plane into two halves, or half-planes

Definition: Half-Plane