Question

When graphing a linear inequality, when can you NOT use (0, 0) as a test point to determine which side of a boundary line to shade?

When the point (0, 0) is on the boundary line.
When the point (0, 0) is below the boundary line.
When the point (0, 0) is above the boundary line.
When the point (0, 0) is part of the solution.

Answer 1

when the point (0,0) is on the boundary line

Answer 2

1. When the point (0, 0) is on the boundary line.

Explanation:

We know that,

'Zero Test' states that 'After substituting the point (0,0) in the inequality, if the result is true, then the solution region is towards the origin. If the result is false, then the solution region is away from the origin'.

So, we see that,

This test holds only if the point (0,0) does not lie on the boundary line of the inequality.

Since, then the expression 'towards the origin and away from the origin' will not make sense.

Hence, (0,0) cannot be used as test point if it lies on the boundary line.