Parametric equation of a line through 2 points
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If you want to see all of the following steps at once, click the "All Steps" button. Otherwise, use the "Next" button.
Find the parametric equations for a line passing through
State the general form of the parametric equation for the
x
-coordinate of a line through the point
.
Which point should we use as point 1?
It doesn’t matter.
Take point P as point 1. Find the parametric equation for
x
.
We get
State the general form of the parametric equation for the
y
-coordinate of a line through the point
.
Take point P as point 1 again. Find the parametric equation for
y
.
We get
As a check, let’s solve for y as a function of x to see if the equation is that of a straight line. First express
t
in terms of
x
.
We found
, so
Substitute this expression into the equation for
y
.
Now let’s check the claim above that either point could be used for point 1. Take point Q as point 1. Find the parametric equation for
x
. Use
u
as the parameter.
We get
State the general form of the parametric equation for the
y
-coordinate of a line through the point
.
Take point Q as point 1 again.
Find the parametric equation for
y
.
We get
As a check, let’s solve for y as a function of x to see if the equation is that of a straight line. First express
u
in terms of
x
.
We found
, so
Substitute this expression into the equation for
y
.
So we do get the same rectangular equation, even though the parameter is different and the parametric equations are different.
Next let’s do a graphical check. Try to plot the two points without using your graphing calculator. Then check your work by clicking “Next”.
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Now add the line through the points. Again click “Next” to check your work.
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Does the line agree with equation above?
Yes, its slope is
and the
y
-intercept is 4.
The end. If you found this helpful and would recommend that I create more pages like this one, please let me know:
Email to John Taylor
General Contents
Detailed Contents
Index