SOLUTION: Find an equation for the linear function f for which f(3)=7 and f(-1)=5.

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Question 553253: Find an equation for the linear function f for which f(3)=7 and f(-1)=5.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

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=3 and y%5B1%5D=7.
Also, is the second point . So this means that x%5B2%5D=-1 and y%5B2%5D=5.


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


m=%285-7%29%2F%28-1-3%29 Plug in y%5B2%5D=5, y%5B1%5D=7, x%5B2%5D=-1, and x%5B1%5D=3


m=%28-2%29%2F%28-1-3%29 Subtract 7 from 5 to get -2


m=%28-2%29%2F%28-4%29 Subtract 3 from -1 to get -4


m=1%2F2 Reduce


So the slope of the line that goes through the points and is m=1%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-7=%281%2F2%29%28x-3%29 Plug in m=1%2F2, x%5B1%5D=3, and y%5B1%5D=7


y-7=%281%2F2%29x%2B%281%2F2%29%28-3%29 Distribute


y-7=%281%2F2%29x-3%2F2 Multiply


y=%281%2F2%29x-3%2F2%2B7 Add 7 to both sides.


y=%281%2F2%29x%2B11%2F2 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation that goes through the points and is y=%281%2F2%29x%2B11%2F2


If you need more help, email me at jim_thompson5910@hotmail.com

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Jim