SOLUTION: Please help me solve: The points (1, 2), (3, 7), and (10, t) lie on the same line. Find the value of t.

Algebra ->  Linear-equations -> SOLUTION: Please help me solve: The points (1, 2), (3, 7), and (10, t) lie on the same line. Find the value of t.      Log On


   

Question 261982: Please help me solve: The points (1, 2), (3, 7), and (10, t) lie on the same line. Find the value of t.
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Here are the steps
step 1 - find the slope between (1, 2), (3, 7) using slope formula as
m+=+%28y2-y1%29%2F%28x2-x1%29
we get
m+=+%287-2%29%2F%283-1%29
so
m+=+5%2F2
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now the slope between (3,7) and (10,t) must have the same slope to be colinear. Again, using the slope formula, we get
m+=+%28y2-y1%29%2F%28x2-x1%29
and then
%285%2F2%29+=+%28t-7%29%2F%2810-3%29
we simplify to get
%285%2F2%29+=+%28t-7%29%2F%287%29
cross multiply to get
35+=+2t+-+14
adding 14 we get
49+=+2t
dividing by 2 we get
t+=+49%2F2