SOLUTION: find linear function f given f(2)=3 and f(6)=4 Im lost not how to do

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Question 1036485: find linear function f given f(2)=3 and f(6)=4
Im lost not how to do
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
find linear function f given f(2)=3 and f(6)=4
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You have two points:: (2,3) and (6,4)
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Form:: y = mx + b
slope = m = (4-3)/(6-2) = 1/4
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Solve for "b" using (2,3) and m = 1/4
3 = (1/4)2 + b
3 = (1/2) + b
b = 5/2
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Equation:
y = (1/2)x + (5/2)
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Cheers,
Stan H.
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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the general form of the linear
equation be:
+f%28x%29+=+a%2Ax+%2B+b+
----------------
given:
(1) +f%282%29+=+a%2A2+%2B+b+
(2) +f%286%29+=+a%2A6+%2B+b+
------------------
Also given:
+f%282%29+=+3+
(1) +3+=+a%2A2+%2B+b+
and
+f%286%29+=+4+
(2) +4+=+a%2A6+%2B+b+
------------------
Rewrite (1) and (2)
(1) +2a+%2B+b+=+3+
(2) +6a+%2B+b+=+4+
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subtract (1) from (2)
(2) +6a+%2B+b+=+4+
(1) +-2a+-+b+=+-3+
-------------------
+4a+=+1+
+a+=+1%2F4+
-------------
and
(1) +2%2A%281%2F4%29+%2B+b+=+3+
(1) +1%2F2+%2B+b+=+3+
(1) +1+%2B+2b+=+6+
(1) +2b+=+5+
(1) +b+=+5%2F2+
---------------------
So, the linear equation is:
+f%28x%29+=+%281%2F4%29%2Ax+%2B+5%2F2+
----------------------
check:
+f%282%29+=+3+
+x+=+2+
+%281%2F4%29%2A2+%2B+5%2F2+=+3+
+1%2F2+%2B+5%2F2+=+3+
+6%2F2+=+3+
+3+=+3+
----------------------
+f%286%29+=+4+
+x+=+6+
+%281%2F4%29%2A6+%2B+5%2F2+=+4+
+3%2F2+%2B+5%2F2+=+4+
+8%2F2+=+4+
+4+=+4+
OK