Question

Two variables are proportionally related with a constant of proportionality r. Which of the following points must lie on the graph of this relationship?

a) (0, r)
b) (0, 0)
c) (1, 1)
d) (r, 1)

Answer 1

The only point that must lie on the graph when two variables are directly proportional with a constant of proportionality r is (0, 0), because any number times zero equals zero.

Step-by-step explanation:

When two variables are directly proportional, their relationship can be described with the equation y = rx, where r is the constant of proportionality. This means that if you plug in x = 0, you would get y = r * 0 = 0. Thus, the only point that must lie on the graph of this relationship is (0, 0) since any number times zero is zero. Points (0, r), (1, 1), and (r, 1) do not provide conclusive information about the value of r and thus, we cannot say that they must lie on the graph without further information on the value of r.