Question

Consider the following sets:

U = {points on the coordinate plane}

A = {solutions to the equation y = 2x + 5}

B = {points on the line y = mx}



For what value of m does A ∩ B = ∅?

m =

Answer 1

m = 2

Reason: Points in A∩B must satisfy m x = 2x + 5, so (m−2)x = 5. If m ≠ 2 this gives x = 5/(m−2) (a solution). If m = 2 the equation becomes 0 = 5, impossible, so no intersection. Equivalently, y = 2x + 5 and y = 2x are parallel distinct lines when m = 2.