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
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.