Question

If y varies directly with x, and $y=0.7$ when $x=0.4$, how do you write the direct linear variation equation?

Answer 1

Hint: To solve this question first we will write the direct variation linear equation for x and y where y is directly proportional to x. then by substituting the values of x and y and simplifying the obtained equation we will get the desired answer.

Complete step-by-step answer:
We have been given that y varies directly with x, and $y=0.7$ when $x=0.4$.
We have to write the direct linear variation equation.
We know that if x varies directly with y it means the relation between x and y is linear in nature.
We have given y varies directly with x i.e. y is directly proportional to x.
We can write it in mathematical form as
$\Rightarrow y\propto x$
Now, we can also write the above equation as
$\Rightarrow y=kx$, where k is the proportionality constant.
Now, substituting the values we will get
$\Rightarrow 0.7=k\times 0.4$
Now, simplifying the above obtained equation we will get
$\begin{align}
  & \Rightarrow \dfrac{0.7}{0.4}=k \\
 & \Rightarrow k=\dfrac{7}{4} \\
\end{align}$
Now, the required equation of variation will be
$\begin{align}
  & \Rightarrow y=\dfrac{7}{4}x \\
 & \Rightarrow 4y=7x \\
\end{align}$
Hence above is the required equation of linear variation.

Note: The point to be noted is that the proportionality constant belongs to the real numbers. In direct variation if the value of one variable changes then the resulting variable value changes in the same proportion. If one value increases another value also increases and vice versa.