PARAMETRIC EQUATION OF A STRAIGHT LINE

A straight line is a very simple "curve" and is, therefore, a good starting point to discuss the development of a parametric representation.

Examination of this line shows the slope to be 2 and the equation of the line in slope intercept form is

which can be written in standard form as

Note that these equations describe the infinite line that passes through the points ( 2, 1 ) and ( 4, 5 ). We are interested only in the line segment between these points. Typically, a parametric curve is defined so that the parameter varies from 0 to 1 over the length of the curve.

Therefore, the above line should be written in parametric form

For the specific line above