SOLUTION: Find the real number n so that the given three points are collinear: (6,3), (n,-1), and (-3,-3)

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Question 29033: Find the real number n so that the given three points are collinear: (6,3), (n,-1), and (-3,-3)
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Here's one approach:
First, find the slope of the line using two of the known points.
Then you can use the slope formulam+=+%28y2-y1%29%2F%28x2-x1%29 to find the value of n.
m+=+%28y2-y1%29%2F%28x2-x1%29 Use the points (6, 3) and (-3, -3) as (x1, y1) and (x2, y2)
m+=+%28-3-3%29%2F%28-3-6%29
m+=+%28-6%29%2F%28-9%29
m+=+2%2F3
Now use the slope formula again, only this time, use the point (n, -1) as one of the two points. The other point can be either one of the other two. Use (6, 3). Using (n, -1) and (6, 3)
m+=+%283-%28-1%29%29%2F%286-n%29
m+=+4%2F%286-n%29 But m+=+2%2F3, so
4%2F%286-n%29+=+2%2F3 Multiply both sides by (6-n)
4+=+2%286-n%29%2F3 Multiply both sides by 3.
12+=+2%286-n%29 Divide both sides by 2.
6+=+6-n Subtract 6 from both sides.
0+=+-n or n+=+0