Question

Given that y varies directly with x and x=6, y=102. How do you write a direct variation equation that relates x and y?

Answer 1

Hint: Here we are given that y varies directly with x. this is nothing but they are in proportion. Also values of x and y are given such that the relation of variation between them can be obtained. This relation is obtained by dividing the value of y given by x. We can say that this division will give the relation or proportion ratio between x and y.

Complete step by step solution:
Given that y varies directly with x.
Such that \[y \propto x\] .
Now we need to find the relation in expression or we can say relation form.
So we will divide the value of y by x.
\[\dfrac{y}{x} = \dfrac{{102}}{6}\]
On dividing we get,
\[\dfrac{y}{x} = 17\]
Taking x on right side we get,
\[\Rightarrow y = 17x\]
This is the relation so obtained. Such that y is 17 times of x.
So, the correct answer is “ \[y = 17x\] ”.

Note: Note that value of x is smaller than value of y. That is why y is 17 times of x. Also note that they are in direct proportion such that if value of x increases the value of y also increases.
If we are asked the relation in y form we can say that it is like \[x = \dfrac{y}{{17}}\]
Both relations are the same. Only the difference is one given x as independent variable \[y = 17x\] and the other gives y as independent variable \[x = \dfrac{y}{{17}}\] .