SOLUTION: If f(x) is a linear function such that f(0)=48 and f(2)=0, identify the slope m of the appropriate straight line.

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Question 494901: If f(x) is a linear function such that f(0)=48 and f(2)=0, identify the slope m of the appropriate straight line.
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
If f(x) is a linear function such that f(0)=48 and f(2)=0, identify the slope m of the appropriate straight line.
Three things you first need to realize are these:

1.  "f(x)" is the same as "y".
2.  f(0)=48 is the same as "(0,48) is a point on the line of the graph of f(x)".
3.  f(2)=0 is the same as "(2,0) is a point on the line of the graph of f(x)".

So the problem is the same as:

Find the equation of the line through the two points (0,48) and (2,0).

Use the slope formula m = %28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 with (x%5B1%5D,y%5B1%5D) = (0,48) and (x%5B2%5D,y%5B2%5D) = (2,0)


m = %28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
m = %28%280%29-%2848%29%29%2F%28%282%29-%280%29%29
m = %28-48%29%2F%282%29
m = -24

Then we use the point-slope formula for the equation of a line,
which is 

y - y1 = m(x - x1)

y - (48) = (-24)(x - 0)
  y - 48 = -24x
       y = -24x + 48

Finally we replace "y" by "f(x)":

    f(x) = -24x + 48 
       
Edwin