Question

If only two points are needed to determine a line why are three ordered pair solutions or points found for a linear equation

Answer 1

Two points give you a line. A third point (often called a check-point) is used to confirm the accuracy of your first two points. If all three line up, you have confirmed you have the correct line.

Answer 2

For any two points that we have, we can find a line that passes through them, so the first part is true, only two points are needed to determine a line.

Then you say:

"why are three ordered pair solutions or points found for a linear equation"

A linear equation is something of the form:

y = a*x + b

Where we assume that you know a and b.

Given that case, we can see that we have infinite solutions.

Suppose that you want to solve this for y, then for each possible value of x you will have a different solution, and you can have infinite values of x there, so there are infinite solutions.

Now, what I think you are asking is:

Why we should use 3 points to check if a relation is linear or not?

Well, exactly for the first thing you said. We always can find a line that passes through two given points, but that is not the case for 3 given points.

So, if in a given relation we use 3 points, and we can see that these are collinear, then we can conclude that the relationship gives a linear equation (ideally you could use more than 3 points, but usually is enough)

If you want to learn more, you can read:

https://brainly.com/question/2263981