SOLUTION: What is a function that has the values f(1)=8 and f(7)=-10

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Question 254011: What is a function that has the values f(1)=8 and f(7)=-10
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since f(1)=8 and f(7)=-10, this means that the line goes through the points (1,8) and (7,-10)




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=1 and y%5B1%5D=8.
Also, is the second point . So this means that x%5B2%5D=7 and y%5B2%5D=-10.


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


m=%28-10-8%29%2F%287-1%29 Plug in y%5B2%5D=-10, y%5B1%5D=8, x%5B2%5D=7, and x%5B1%5D=1


m=%28-18%29%2F%287-1%29 Subtract 8 from -10 to get -18


m=%28-18%29%2F%286%29 Subtract 1 from 7 to get 6


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-8=-3%28x-1%29 Plug in m=-3, x%5B1%5D=1, and y%5B1%5D=8


y-8=-3x%2B-3%28-1%29 Distribute


y-8=-3x%2B3 Multiply


y=-3x%2B3%2B8 Add 8 to both sides.


y=-3x%2B11 Combine like terms.


y=-3x%2B11 Simplify


So the equation that goes through the points and is y=-3x%2B11


This means that the function is f%28x%29=-3x%2B11 (replace 'y' with f(x))


Notice how the graph of y=-3x%2B11 goes through the points and . So this visually verifies our answer.


Graph of y=-3x%2B11 through the points and