Provide an appropriate response.Explain how the sign of B determines whether you would shade above or below the boundary line in graphing Ax + By > C.

Question

What will be an ideal response?

Answer 1

Answers may vary. One possibility: The answer depends on whether the equation resolves to y > f(x) or y < f(x). To solve the inequality, first subtract Ax from both sides, yielding By > C - Ax. The next step is the key to the question. To isolate y, divide each side by B. If B is positive (that is, B > 0), then there is no change to the inequality sign. However, if B has a negative sign (that is, B < 0), then the sign reverses. In the first case, you would shade above the boundary line; in the second, you would shade below. (Alternately, you could begin solving the equality by subtracting B from each side if the sign of B is negative. This would avoid division of the inequality by a negative number.)