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Question 156168: I have one more problem that hopefully you'll be able to help me;
If f(4)=0 and f(6) =6, which of the following could represent f(x)?
A. 2/3x-4
B. x+2
C. x-4
D. 3/2x+6
E. 3x-12
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! The statement  tells us that if  , then  . So the point (4,0) is on the line. Also, the statement  tells us that if  , then  . So the point (6,6) is also on the line.
So let's find the equation of the line that goes through the two points (4,0) and (6,6)
To do that, we first need to find the slope of the line through the points ) and )
 Start with the slope formula.
 Plug in  ,  ,  , and 
 Subtract  from  to get
 Subtract  from to get 
 Reduce
So the slope of the line that goes through the points and is
Now let's use the point slope formula:
 Start with the point slope formula
 Plug in , , and
 Distribute
 Multiply
 Add 0 to both sides.
 Combine like terms.
Simplify
So the equation that goes through the points and is
In function notation, the answer is 
Notice how  and  . So this also verifies our answer.
Also, notice how the graph of goes through the points and . So this visually verifies our answer.
 Graph of through the points and
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