What will this site do for you?

This site will determine the line that goes through the two given points.

There are 4 possible outcomes:

• A function that defines a line through the given points
• A constant function if y₁ and y₂ are equal
• A parameterized family of functions if the points are equal
• A relation as x₁ and x₂ are equal

So you see there are three special cases and one regular case you have to be aware of.

One case is even more strange: You won't get a function, but a relation to describe the line. The point is that a function has only one input value per output value. This constraint is violated if you provide points that have both y equal.

Families of functions have additional parameters aside to the independent variable (x). This case occur if you provide only one point. It is clear that the result set of functions that matches the criteria to pass this point is infinite. So you have two possibilities to formulate the function. Either you vary the slope (a) or the intersection with the x-axis. After all it doesn't matter which way you choose.

Two points line

Calculates function parameters for a line that goes through two points.