F3 Physics question. urgent!!!

Let y cm be the column length at 37oC.


Method 1:

(Change in length from 0oC to 80oC) / (Change in temp from 0oC to 80oC)
= (Change in length from 0oC to 37oC)/(Change in temp from 0oC to 37oC)

(21 - 6) cm / (80 - 0)oC = (y - 6) cm / (37 - 0)oC

15/80 = (y - 6)/37

80(y - 6) = 15 x 37

80y - 480 = 555

80y = 1035

y = 12.94

Hence, the column length at 37oC = 12.94 cm


Method 2:

(Change in length from 0oC to 80oC) / (Change in temp from 0oC to 80oC)
= (Change in length from 37oC to 80oC)/(Change in temp from 37oC to 80oC)

(21 - 6) cm / (80 - 0)oC = (21 - y) cm / (80 - 37)oC

15/80 = (21 - y)/43

80(21 - y) = 15 x 43

1680 - 80y = 645

80y = 1035

y = 12.94

Hence, the column length at 37oC = 12.94 cm

The Length for 37℃:
T = 80℃ x [ L-L(0℃) / L(80℃) - L(0℃) ]
37℃ = 80℃ x [ ( L - 6 ) / ( 21 - 6 ) ]
37℃ ( 21-6 ) = 80℃ x ( L - 6 )
555 = 80℃ x ( L - 6 )
6.9375 = L - 6
L = 12.9375 cm
= 12.9 cm ( In physics , answers are always correct to 3 significant figures ) (準確至三位有效數字)

First , I need you to understand how does the formula work.
T = Temperature , L = Length
On right hand side,
80℃ x [ L-L(0℃) / L(80℃) - L(0℃) ]
L(80℃) is the length of the temperature in 80℃
L(0℃) is the length of the temperature in 0℃
L is the unknown value that you are going to find out.
L-L(0℃) / L(80℃) - L(0℃) means that the specific value of the temperature and the length. ( 長度與溫度的比值)
Use 80℃(the upper temperature in the question) times the specific value
Then we can finally find that it is 37℃ ( = left hand side)
After calculating it, we can find out the length for 37℃is 12.9cm.
So , the formula of the relation of temperture and length is
　　　　 L - L (lower temp.)
T = T(upper temp.) x ----------------------------------------------
　　　　 L(upper temp.) - L (lower temp.)