Question

The solution of a linear inequality in two variables is a (half-plane/test point).

A) Half-plane
B) Test point

Answer 1

The solution of a linear inequality in two variables is a half-plane. It can be represented by shading a portion of the coordinate plane based on the inequality symbol.

Step-by-step explanation:

The solution of a linear inequality in two variables is a half-plane. A half-plane is a region in the coordinate plane that satisfies the inequality. It can be represented by shading a portion of the plane either above or below the boundary line, depending on the inequality symbol.

For example, if the inequality is y < mx + b, the half-plane would be shaded below the line y = mx + b. To determine which half-plane to shade, one can choose a test point that is not on the boundary line and substitute its coordinates into the inequality.

If the inequality is true for the test point, then the shaded region is the solution. If the inequality is false for the test point, then the opposite half-plane is the solution.