Question

Let y vary directly as x, if y = 12 when x = 4, then write a linear equation. What is the value of y when x = 5?

Answer 1

Hint: Assume that y is directly proportional to x. Remove the proportionality and assume a constant ‘k’ in place of that. Now, substitute the value of x and y given in the question and find the value of constant ‘k’ using this information. Substitute the value of ‘k’ in the original equation to get the required linear equation. Substitute the value of x = 5 to get the required value of y.

Complete step by step answer:
We have been provided with the information that y is varying directly as x and we have to form a linear equation.
We know that, a linear equation is given as: - \[y=mx+c\], where m = slope, c = intercept of line of y – axis.
In the question, it is only said that y varies directly as x and nothing is given about the intercept. So, will assume that y is directly proportional to x.
Now, when we remove the proportionality sign, we assume of constant in place of that. Let that constant be ‘k’.
\[\Rightarrow y=kx\] - (1)
Also, we have provided that when x = 4 then y = 12.
Therefore, substituting these values of x and y in equation (i), we get,
\[\begin{align}
  & \Rightarrow 12=k\times 4 \\
 & \Rightarrow k=\dfrac{12}{4} \\
 & \Rightarrow k=3 \\
\end{align}\]
So, the value of proportionality constant is k = 3, so the required linear equation is given by: -
\[\Rightarrow y=3x\]
Now, we have to find the value of y when x = 5. Therefore, substituting x = 5 in above equation, we have: -
\[\begin{align}
  & \Rightarrow y=3\times 5 \\
 & \Rightarrow y=15 \\
\end{align}\]

So, the correct answer is 15.

Note: Remember that we do not have to get confused, as we have been asked to write a linear equation and we assume it as \[y=mx+c\], because there is only one information given from which we can find only one variable. Also, note that for solving the \[{{2}^{nd}}\] part of the question we need to find the value of ‘k’ just as we did above.