SOLUTION: Let f be a linear function. If f(−2) = −2 and f(4) = −20, find f(x). f(x)=

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Question 1133367: Let f be a linear function. If
f(−2) = −2
and
f(4) = −20,
find
f(x).
f(x)=
Found 2 solutions by josgarithmetic, math_helper:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Points (x,y) are (-2, -2) and (4, -20).

Slope, %28-20%2B2%29%2F%284%2B2%29=-18%2F6=-3

Take either point to setup an equation:
-3=%28y-%28-2%29%29%2F%28x-%28-2%29%29
-3=%28y%2B2%29%2F%28x%2B2%29
y%2B2=-3%28x%2B2%29
y=-3x-6-2
y=-3x-8

as function, highlight%28f%28x%29=-3x-8%29

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!

The linear function goes through (-2,-2) and (4,-20):
f(x) = mx + b

m = (-20-(-2))/(4-(-2)) = -18/6 = -3

f(x) = -3x + b

Using (-2,-2), solve for b:
-2 = -3(-2) + b
-8 = b

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Ans: +highlight%28f%28x%29+=+-3x+-+8%29+
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Check: f(-2) = -3(-2)-8 = 6-8 = -2 (ok)
and f(4) = -3(4)-8 = -12-8 = -20 (ok)