Parametric Curves


Problem: Write parametric equations of a line segment through (7,5) with slope of 3. Graph the line segments using your equations.


Recall the point-slope form for the equation of a line is   .


If I let x=t, then  and we obtain the parametrization  



I can obtain another parametrization for the line if I let  


In this case  and I have


I know that a pair of parametric equations is a pair of continuous functions that define the x and y coordinates of a point in a coordinate plane in terms of a third variable, such as t, called the parameter.


Thus, a parametric curve in the plane is a pair of functions


x= f(t)

y= g(t)


where the two continuous functions define ordered pairs (x,y).

So my substituting into:  we get:    



Now, letŐs check this out. When I put these back into point-slope form I obtain the following:


               y-5 = 3(x-7)

               y=3x - 21 + 5



Now, letŐs see if our calculations are correct.


LetŐs graph y=3x-16




Now, letŐs graph   and pray that itŐs the same graph.



Yes, both graph the same line, so my calculations were correct.