Find the linear equation that expresses temperature in degrees Celsius as a function of temperature in degrees

Question

fahrenheit

Answer 1

F = 9/5 C + 32

SO

C = 5/9 F - 32

Answer 2

The melting point of water is 0ºC or 32ºF and the boiling point of water is 100ºC or 212ºF. These are both linear scales.

To find the linear relationship between them, set up Cartesian coordinates with ºC on the Y-axis and ºF on the X-axis.

Then plot the 2 points (32, 0) and (212, 100) and draw a line through them.

The equation to this line is C = mF + b in similar fashion to the general straight-line equation y = mx + b, where m is the slope and b is the y-intercept.

Let (x1, y1) = (32, 0) and (x2,y2) = (212, 100)

The slope is given by m = (y2 - y1) / (x2 - x1)
= (100 - 0) / (212 - 32)
= 100 / 180
= 5 / 9.

The y-intercept is given by b = (x2*y1 - x1*y2) / (x2 - x1)
= (212*0 - 32*100) / (212 - 32)
= - 3200 / 180
= - 160 / 9

Now the relationship is
C = (5/9)F - 160/9
= (5F - 160) / 9
= 5(F - 32) / 9

This then, is the expression showing ºC as a function of ºF.

Answer 3

F = 9/5C + 32

C = (F -32)x 5/9

Answer 4

0.555(degree F-32)=degrees C
(1.8 x degree C)+32=degrees F