Question

How do you name the constant of variation in the equation, \[y = 4x?\]

Answer 1

Hint: In these types of problems in which we have to find a constant of variation or name the constant of variation first we try to find out which is the dependent variable and which is the independent variable. After identifying both we start to put different values in the place of the independent variable and start obtaining values of the dependent variable. At last, we check the variation which takes place among all obtained values of dependent variables. The variation which we obtain can be taken as constant of variation.

Complete step by step answer:
First, we are writing the above given equation as following,
\[ \Rightarrow y = 4x\]
Now try to identify dependent and independent variables. As four is multiplying with the variable \[x\]and for any value of \[x\],\[y\] is giving the output value. It simply means that \[y\] is depending on \[x\]. Therefore, \[x\] is an independent variable and \[y\] is a dependent variable.
After identifying the dependent and the independent variables, we are going to put the different values of \[x\] for which different values of \[y\] can be obtained.
Putting \[x = 1\], we get
\[ \Rightarrow y = 4 \times 1\]
\[ \Rightarrow y = 4\]
Putting \[x = 2\], we get
\[ \Rightarrow y = 4 \times 2\]
\[ \Rightarrow y = 8\]
Putting \[x = 3\], we get
\[ \Rightarrow y = 4 \times 3\]
\[ \Rightarrow y = 12\]
Putting \[x = 4\], we get
\[ \Rightarrow y = 4 \times 4\]
\[ \Rightarrow y = 16\]
So, after putting \[x = 1,2,3\] and \[4\], we got the \[y = 4,8,12\] and \[16\] respectively. By seeing these values, we are clearly identifying that for each value of \[x\], values of \[y\] are the multiples of \[4\]. That means \[4\] is the constant value that is coming in each obtained value of \[y\].

Therefore, we can say that \[4\] is the constant of variation in the above given equation.

Note: Constant of variation is defined as it is the constant ratio of two variable quantities. i.e., for every change of \[1\] unit of ‘\[x\]’ how many units of change are obtained in\[y\].