SOLUTION: Find the parametrized form of the line through (5, -2) and (8, 2).

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Question 1133321: Find the parametrized form of the line through (5, -2) and (8, 2).
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


There are an infinite number of parameterized forms of the equation....

The slope-intercept form of the equation through the two given points is

y+=+%284%2F3%29x-26%2F3

An equivalent equation is then

3y+=+4x-26

or

4x-3y+=+26

From this form, we can see that any parameterized form has to be of the form

y+=+4t%2Ba
x+=+3t%2Bb

If we let t=0 correspond to the point (5,-2), then the parameterized equations are

y+=+4t-2
x+=+3t%2B5

If we let t=0 correspond to the point (8,2), then the parameterized equations are

y+=+4t%2B2
x+=+3t%2B8

And of course we can get other parameterized equations by letting t=0 correspond to some other point on the line through the two given points.