How can you determine the parametric equation of a line?

Determining the parametric equation of a line requires you to know at least two points on the line. This calculus-based equation can be used to prove that another given point is on that same line. This theorem states that with two given points (x1, y1) and (x2, y2), a third point (x, y) is on the line with these two points only if there is a real number "t" that satisfies the following equations: x = (1-t)x1 + tx2 and y = (1-t)y1 + ty2.

1. Determine the two points on a line

   Find two points on a line and record them as x-y coordinates. In cases where it is a straight line, it may be oriented such that the x and y values are all equal to zero. In a word question, these will most likely be given.

2. Select the value for "t"

   Select a value for "t" that is a real number. A real number can be rational or irrational, but it can't be imaginary. An example of an imaginary number would be the root of a negative number.

3. Insert the values into the equations

   Insert the values of "t", (x1, y1) and (x2, y2) into the parametric equations to determine the value of point (x, y).