Inverse Proportion

Imagine traveling in some vehicle while the roads are quite empty, without any traffic jams.

As you travel more kilometers and more time passes, the amount of gasoline decreases.

We can say that, as the distance increases the amount of gasoline decreases.

Let's see a graphical representation of inverse proportionality:

The function: $Y=\frac{a}{X}$

represents inverse proportionality.

As the $X$ increases the $Y$ decreases.

To find out if there is inverse proportionality, we will examine if, when one term is multiplied by a certain amount of times, the second term is decreased by the same amount of times.

Given the following table:

Let's check if every time $X$ increases by a specific amount, $Y$ also decreases in the same proportion.

If this occurs, it means there is inverse proportionality. If not, then there isn't.

Let's ask:

By how much does $X$ increase from $5$ to $10$?

The answer is it multiplies by $2$.

And by how much does $Y$ decrease from $20$ to $10$?

The answer is it divides by $2$.

Let's continue,

By how much does $X$ increase from $5$ to $20$? The answer is it multiplies by $4$.

And by how much does $Y$ decrease from $20$ to $5$?

The answer is it divides by $4$.

We will continue examining and discover that indeed every time $X$ multiplies by a certain number, $Y$ also decreases divided by the same number.

We will see it in the following way: