SOLUTION: If f(4) = 0 and f(6) = 6, which of the following could represent f(x)? A 2/3x - 4 B 5+2 C x-4 D 3x-12 I want to understand how to solve this problem. Thanks, Stacy

Algebra ->  Functions -> SOLUTION: If f(4) = 0 and f(6) = 6, which of the following could represent f(x)? A 2/3x - 4 B 5+2 C x-4 D 3x-12 I want to understand how to solve this problem. Thanks, Stacy      Log On


   

Question 288657: If f(4) = 0 and f(6) = 6, which of the following could represent f(x)?
A 2/3x - 4
B 5+2
C x-4
D 3x-12
I want to understand how to solve this problem.
Thanks,
Stacy
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If f(4) = 0 and f(6) = 6, this means that the equation is a straight line that goes through the points (4,0) and (6,6).

Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (4,0) and (6,6)


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: (x%5B1%5D,y%5B1%5D) is the first point (4,0) and (x%5B2%5D,y%5B2%5D) is the second point (6,6))


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 (these are the coordinates of given points)


m=+6%2F2 Subtract the terms in the numerator 6-0 to get 6. Subtract the terms in the denominator 6-4 to get 2




m=3 Reduce



So the slope is

m=3





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Now let's use the point-slope formula to find the equation of the line:




------Point-Slope Formula------
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and (x%5B1%5D,y%5B1%5D) is one of the given points


So lets use the Point-Slope Formula to find the equation of the line


y-0=%283%29%28x-4%29 Plug in m=3, x%5B1%5D=4, and y%5B1%5D=0 (these values are given)



y-0=3x%2B%283%29%28-4%29 Distribute 3


y-0=3x-12 Multiply 3 and -4 to get -12%2F1. Now reduce -12%2F1 to get -12

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


y=3x-12 Combine like terms -12 and 0 to get -12

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Answer:



So the equation of the line which goes through the points (4,0) and (6,6) is:y=3x-12


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=3 and the y-intercept is b=-12


Notice if we graph the equation y=3x-12 and plot the points (4,0) and (6,6), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=3x-12 through the points (4,0) and (6,6)


Notice how the two points lie on the line. This graphically verifies our answer.





So the equation of the line that goes through the points (4,0) and (6,6) is y=3x-12. Just replace the 'y' with 'f(x)' to get f%28x%29=3x-12. So the answer is D)