Direct and Inverse Variation Table

Question

The table shows the variation between a, b, c, and d. Complete the table.

a with b              b with c            c with d            a with d

direct              direct               inverse

a with d is inverse or direct?

Answer 1

Intuitively, I would say a varies inversely with d, but let's not rely on intuition.

When we say a varies directly with b, we mean

1) a = k₁b,

2) b = k₂c.

By inverse variation we mean

3) c = k₃ / d k_1, k₂, k₃ are constants.

So, substitute equation 2 in to equation 1 to get a = k₁k₂c.

Now substitute 3) into the equation on the previous line to get a = k₁k₂k₃/d.

As k₁k₂k₃ is a constant, then a varies inversely with d.