SOLUTION: 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 Now i no the answer is "E" because someone told me but the

Question 151659: 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

Now i no the answer is "E" because someone told me but they didn't explain it good enough so i was wandering if you could give it a try?
Thank you!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If f(4)=0, then x=4 and y=0. Also if f(6)=6, then x=6 and y=6

So the equation goes through the points (4,0) and (6,6)

First let's find the slope of the line through the points

and

Start with the slope formula.

Plug in , , , , ,

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

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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