Question

If $a$varies directly as $b$and $a=16$, when $b=4$. Find the equation that relates $a$ and $b$.

Short answer

The equation relating$a$and$b$is$a=4b$.

Step-by-step solution

Step 1. Given information

Given that$a$varies directly as$b$and$a=16$when$b=4$.

Equation relating a and b.

Since $a$varies directly as $b$, therefore

$$\begin{gathered} a\alpha b \\ \Rightarrow a=kb\to \left(1\right) \end{gathered}$$

Now since $a=16$when $b=4$, therefore from equation (1) we get

$$\begin{gathered} 16=k·4 \\ \Rightarrow k=4 \end{gathered}$$

Now put $k=4$in equation (1), we get

$a=4b$