SOLUTION: Find a linear model for the given set of data. Explain your thinking process in arriving at the equation. x -2 0 1 3 4 f(x) 8 2 -1

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Question 28497: Find a linear model for the given set of data. Explain your thinking process in arriving at the equation.
x -2 0 1 3 4
f(x) 8 2 -1 -7 -10
Please help
Thank you very much
Answer by venugopalramana(3286) About Me  (Show Source):
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Find a linear model for the given set of data. Explain your thinking process in arriving at the equation.
x -2 0 1 3 4
f(x) 8 2 -1 -7 -10
SINCE IT IS A LINEAR MODEL IT MEANS F(X)=AX+B = Y...SAY ..WHERE A AND B ARE CONSTANTS..SO PUT ANY 2 SETS OF VALUES FOR X AND Y AS GIVEN IN THE ABOVE EQUATION AND FIND A AND B.LET US TAKE
x -2 0
f(x) 8 2
SO WE GET
8=A*(-2)+B..................I
2=A*0+B..........II...OR B=2...SUBSTITUTING IN I WE GET ...
8=-2A+2
2A=2-8=-6
A=-3...SO....
Y=F(X)=-3X+2...LET US CHECK FOR OTHER VALUES WHETHER LINEAR MODEL IS CORRECT OR NOT...
X=1....Y=-3+2=-1....OK
X=3....Y=-3*3+2=-7.....OK
X=4....Y=-3*4+2=-10.....OK