A Rational Number is a number that can be made by dividing two integers. We know that an integer is a number with no fractional part. On the other hand, an Irrational Number is a real number that cannot be made by dividing two integers. In this way, its decimal goes on forever without repeating.
If we have a set of six numbers that include both rational and irrational numbers and there are no duplicates among the rational numbers and no duplicates among the irrational numbers, then the conclusion is that we will have exactly 6 points. From the previous definitions we know that none of the rational numbers can also be irrational, or vice-versa. So, the fewest number of distinct points that need to be graphed is either an rational number or an irrational number. In the Figure below there's a representation of this problem. The number in blue are irrational and the red ones are rational.
