Question

Given that y varies directly with x, how do you write a direct variation equation that relates x and y for x = 5, y = 10?

Answer 1

Hint: In solving the questions like this we should go through the given conditions in the question carefully to solve the question. Here it is mentioned that y varies directly with x, from this we can conclude that the relation to be determined is linear in nature. The values of x and y are given as x = 5 and y = 10 so from this we can get the relation between them. From all these calculations we can get the relation between x and y.

Complete step by step solution:
If y varies directly with x, then
y = m \[\times \] x
Here, m is a constant.
We are told that this relation holds for (x, y) = (5, 10)
When we apply the values of x and y from question to the equation mentioned above we can get the value of m.
\[\Rightarrow \] 10 = m \[\times \] 5
\[\Rightarrow \] m = \[\dfrac{10}{5}\]
\[\Rightarrow \] m = 2
From this we got the value of the constant term m, which helps us to get a relationship between x and y.
Now, put the value of m in the above equation, we get,
\[\Rightarrow \] y = 2 \[\times x \]
\[\Rightarrow \] y = 2x
The above equation shows the relation between x and y with the given condition.

Note: It is very important for us to remember the standard equation of a linear form and to find the relationship between the x and y for the given question with the given values. Here, we can also express x in terms of y in the final answer. We must not make the mistake in writing the relation as x = 2y by misinterpreting the data given in the question.