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# Economy cars \$\$ Linear function

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Helo everyone can someone help me to resolve this ?

If f is a linear model for which f(4) = -3 and f(-4) = 21

1. find f(9)

How do I do that ? Can someone show/ explain it to me ?

Guest Nov 1, 2015
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The equation of a straight line can be written as f(x) = m*x + c where m and c are constants found from the given information as follows:

f(-4) = 21  so  21 = -4*m + c    ...(1)

f(4)  = -3  so   -3 = 4*m + c     ...(2)

Add (1) and (2) term by term to get  21 - 3 = -4m + 4m + c + c  or 18 = 2c so c = 9

Put this back into (2) to get  -3 = 4m + 9   so 4m = -12  so m = -3

Hence the straight line function is  f(x) = -3x + 9

Now simply replace x by 9 to work out what f(9) is.

Alan  Nov 2, 2015

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