Question

How do you write direct variation equations?

Answer 1

Hint: To solve this question we will use the concept of proportionality. First we will assume two variables say x and y and assume that x is directly proportional to y. Then by adding the proportionality constant we will write the equation.

Complete step by step solution:
We have to write the direct variation equation.
We know that proportionality in algebra is the equality between two ratios. There are two common proportions: direct and inverse proportion.
Direct variation describes a simple relation between two variables. In two variables one is the constant multiple of the other.
Let us assume two variables say x and y.
Now, let us assume that x constantly varies with respect y i.e. x is directly proportional to y.
We can write it in mathematical form as
$\Rightarrow x\propto y$
Now, we can also write the above equation as
$\Rightarrow x=ky$, where k is the proportionality constant and has real values
Hence above obtained equation is the required direct variation equation.

Note: The point to be noted is that if given that x varies directly with y it means the relation between x and y is linear in nature. We can also express x in terms of y by using the relation between the two. We can easily find the values by using the proportionality equation. The proportionality constant belongs to the real numbers.