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

Algebra ->  Functions -> 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      Log On


   

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) About Me  (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


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%286-0%29%2F%286-4%29 Plug in y%5B2%5D=6, y%5B1%5D=0, x%5B2%5D=6, x%5B1%5D=4, ,


m=%286%29%2F%286-4%29 Subtract 0 from 6 to get 6


m=%286%29%2F%282%29 Subtract 4 from 6 to get 2


m=3 Reduce


So the slope of the line that goes through the points and is m=3


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-0=3%28x-4%29 Plug in m=3, x%5B1%5D=4, and y%5B1%5D=0


y-0=3x%2B3%28-4%29 Distribute


y-0=3x-12 Multiply


y=3x-12%2B0 Add 0 to both sides.


y=3x-12 Combine like terms.


y=3x-12 Simplify


So the equation that goes through the points and is y=3x-12


Notice how the graph of y=3x-12 goes through the points and . So this visually verifies our answer.
Graph of y=3x-12 through the points and