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.
- 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.
- 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.
- 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).