Questions on Algebra: Functions, Domain, NOT graphing answered by real tutors!

Algebra ->  Algebra -> Questions on Algebra: Functions, Domain, NOT graphing answered by real tutors!     (Log On)
Ad: Algebra Solved!™: algebra software that solves YOUR algebra homework problems with step-by-step help!


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!: 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(9166) 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=(y[2]-y[1])/(x[2]-x[1]) Start with the slope formula.


m=(6-0)/(6-4) Plug in y[2]=6, y[1]=0, x[2]=6, x[1]=4, ,


m=(6)/(6-4) Subtract 0 from 6 to get 6


m=(6)/(2) 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[1]=m(x-x[1]) Start with the point slope formula


y-0=3(x-4) Plug in m=3, x[1]=4, and y[1]=0


y-0=3x+3(-4) Distribute


y-0=3x-12 Multiply


y=3x-12+0 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.
drawing( 500, 500, -10, 10, -10, 10,<BR> graph( 500, 500, -10, 10, -10, 10,3x-12),<BR> circle(4,0,0.08),<BR> circle(4,0,0.10),<BR> circle(4,0,0.12),<BR> circle(6,6,0.08),<BR> circle(6,6,0.10),<BR> circle(6,6,0.12)<BR> ) Graph of y=3x-12 through the points and