SOLUTION: What is the linear function f with the given values? F( -4) = -2, f(2) = 7

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Question 822876: What is the linear function f with the given values?
F( -4) = -2, f(2) = 7
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
F( -4) = -2, f(2) = 7 means we have the two points on the line: (-4,-2) and (2,7)


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


Note: is the first point . So this means that x%5B1%5D=-4 and y%5B1%5D=-2.
Also, is the second point . So this means that x%5B2%5D=2 and y%5B2%5D=7.


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


m=%287--2%29%2F%282--4%29 Plug in y%5B2%5D=7, y%5B1%5D=-2, x%5B2%5D=2, and x%5B1%5D=-4


m=%289%29%2F%282--4%29 Subtract -2 from 7 to get 9


m=%289%29%2F%286%29 Subtract -4 from 2 to get 6


m=3%2F2 Reduce


So the slope of the line that goes through the points and is m=3%2F2


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--2=%283%2F2%29%28x--4%29 Plug in m=3%2F2, x%5B1%5D=-4, and y%5B1%5D=-2


y--2=%283%2F2%29%28x%2B4%29 Rewrite x--4 as x%2B4


y%2B2=%283%2F2%29%28x%2B4%29 Rewrite y--2 as y%2B2


y%2B2=%283%2F2%29x%2B%283%2F2%29%284%29 Distribute


y%2B2=%283%2F2%29x%2B6 Multiply


y=%283%2F2%29x%2B6-2 Subtract 2 from both sides.


y=%283%2F2%29x%2B4 Combine like terms.


So the equation that goes through the points and is y=%283%2F2%29x%2B4


Therefore, the function is f%28x%29+=+%283%2F2%29x%2B4