Question

The pressure, p, on a diver varies directly as the depth of the water, d. Using k as the constant of variation, write an equation expressing this relationship. Do not include spaces in your answer. Enter fractions just as you would on the calculator.

Answer 1

p=kd

How can we check this? Well, it states that p varies directly with d. That means that if p increases, so does d.

Another way to think of it is to look at it without the constant k.
p=d
If p=50, then what does d have to be to satisfy the equation? It also has to be 50.
Let's say that p was raised to 70. Then what must d be? That's right, 70 also. This relationship means that as p increases, so does d. And as p decreases, so does d.

Factoring k back in, we say that the expression is:
\[p=kd\]

Answer 2

By no means does that mean that d will be the same value as p. It's a very, VERY simple way to understand if a relationship varies directly or inversely.

In all variation, we must include a constant K, because we are unsure if they are the same values or not.