SOLUTION: What is the linear equation f for which f((1)=10 and f(2)=20

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Question 667213: What is the linear equation f for which f((1)=10 and f(2)=20
Found 2 solutions by ewatrrr, MathLover1:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

What is the linear equation f for which 

f(1)=10  f%28x%29+=+10x

f(2)=20

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
What is the linear equation f for which f%281%29=10 and f%282%29=20

The general form of a linear function is:

f%28x%29=ax+%2B+b

So, f%281%29=10 means that we have to substitute, in the general form,
the unknown x with the value 1.

a%2A1+%2B+b+=+10
a+%2B+b+=+10

now do the same thing with the following f%282%29=20
2a+%2Bb+=+20

in order to find the function f, we have to determine the unknown
coefficients a and b.

now subtract a+%2B+b+=+10 from the 2a+%2Bb+=+20,
2a+%2Bb-%28a%2Bb%29+=+20-10
2a+%2Bb-a-b+=+10
a=+10

With the known value of a, we are going in any of the equations above,
substitute a and find out the value of b unknown.

a+%2B+b+=+10
10+%2B+b+=+10
b+=+10-10
b+=+0

Now we could write down the linear function f:
f%28x%29=10x+%2B0
f%28x%29=10x