SOLUTION: find in terms of t the equation of the line through the point (t,0) with gradient t. find the values of t for which the line passes through the point (5,6)

Algebra ->  Coordinate-system -> SOLUTION: find in terms of t the equation of the line through the point (t,0) with gradient t. find the values of t for which the line passes through the point (5,6)      Log On


   

Question 384718: find in terms of t the equation of the line through the point (t,0) with gradient t. find the values of t for which the line passes through the point (5,6)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the point-slope form of a line, y-y%5Bp%5D=m%28x-x%5Bp%5D%29.
y-0=t%28x-t%29
y=tx-t%5E2
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Now use the point (5,6),
6=t%2A5-t%5E2
t%5E2-5t%2B6=0
%28t-3%29%28t-2%29=0
Two solutions:
t-3=0
t=3
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t-2=0
t=2
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Ahmad, I tried to respond to your question but I got a bounceback. Hopefully you'll look here.
The answer is no.
+t%5E2-6t-t%2B6=t%5E2-7t%2B6 and
+t%5E2-6t-t%2B6%3C%3Et%5E2-5t%2B6
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I made the same mistake in my first solution, then went back to verify and caught the mistake.
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t%5E2-5t%2B6=t%5E2-3t-2t%2B6
t%5E2-5t%2B6=t%28t-3%29-2%28t-3%29
t%5E2-5t%2B6=%28t-3%29%28t-2%29