Estimate linear fx

Which of the following is the best estimate for the temperature at 11 PM if the temperature continues to drop at the same rate?
timetemperature °C
3 PM 32
6 PM30
12 PM20


Correct answer:

t =  21.6667 °C

Step-by-step explanation:

t(x)=a⋅ x+b  30=6⋅ a+b 20=12⋅ a+b  6a+b=30 12a+b=20  Pivot:Row1↔Row2 12a+b=20 6a+b=30  Row2−126​⋅ Row1→Row2 12a+b=20 0.5b=20  b=0.520​=40 a=1220−b​=1220−40​=−1.66666667  a=3−5​≐−1.666667 b=40  t=a⋅ 11+b=(−1.6667)⋅ 11+40=21.6667°C

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