Write a linear function f with the values f(−1)=8 and f(5)=6. A function is f(x)=
1 answer:
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Answer:
f(x) = -1/3x +23/3
Step-by-step explanation:
You can use the linear regression function of a graphing calculator or spreadsheet to show you the equation of the line through these points:
f(x) = -1/3x +23/3
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Approaching this in the usual way, we recognize we have points ...
(-1, 8) and (5, 6)
The slope of the line through those points is ...
m = (y2 -y1)/(x2 -x1)
m = (6 -8)/(5 -(-1)) = -2/6 = -1/3
Then the point-slope equation of the line is ...
y - 8 = -1/3(x +1)
Adding 8 gives us a form we can use for a function definition:
f(x) = -1/3(x +1) +8
f(x) = -1/3x +7 2/3
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