Question

How do you determine whether the equation represents a direct variation if it does, find the constant of variation $2y = 5x + 1$?

Answer 1

Hint: We are given an equation and we have to find whether the question shows direct variation or not. If it shows then we have to find the constant of variation of the equation. Direct variation describes a simple relationship between two variables. We say y varies directly with x if:
Y=kx
For some constant k, called the constant of variation or constant of proportionality.
We will first convert the equation into the form of y=kx. If the equation gets converted into this form then will find a constant i.e. k. If it does not get converted in this form then it will not represent the direct variation.

Complete step-by-step answer:
Step1: We are given an equation $2y = 5x + 1$ and we have to check whether it is a direct variation or not. First we will convert this equation into a relationship that expresses a direct variation i.e. y=kx. Where k is the constant. On converting the equation we will get:
$ \Rightarrow y = \dfrac{5}{2}x + \dfrac{1}{2}$
This line is of the form y=mx+c. On comparing it with the form we get
$ \Rightarrow \left( {y = mx + c} \right) \ne \left( {y = kx} \right)$.
The given equation is not of the form y=kx and so doesn’t represent direct variation.
Step2: As this equation does not represent the direct variation so we will not find the constant of the equation.

Step3: Final answer: Hence the equation doesn’t represent the direct variation.

Note:
In this type of question students may not get an approach how to solve this question. There is only one way to solve such a question that is to compare the equation with the form Y=kx which is an equation of direct variation in which X varies directly with Y. If it is a direct variation than on comparing the equation formed with the equation of a direct variation we will get the value of the constant also.