A math word problem.
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A math word problem.

[From: ] [author: ] [Date: 12-08-09] [Hit: ]
(100 - 0) / (212 - 32) = 100/180 = 5/9. So the line will be of the form C = (5/9)*F + b,where b is the y-intercept, where in this case y corresponds to degrees Celsius.To find b, plug in a known data point,......
Find the equation of the line that shows the relationship between the temperature in degrees Celcius 'C' and degrees Fahrenheit 'F'. Remember that water freezes at 0 degrees Celsius (32 degrees Fahrenheit) and boils at 100 degrees Celsius (212 degrees Fahrenheit).

Please explain step by step.
Thank you so much in advance!!

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So we need to find an equation for C in terms of F. Knowing that 0 degrees Celsius
corresponds to 32 degrees Fahrenheit and 100 degrees Celsius corresponds to
212 degrees Fahrenheit the slope m of the line C = m*F + b will be

(100 - 0) / (212 - 32) = 100/180 = 5/9. So the line will be of the form C = (5/9)*F + b,

where b is the y-intercept, where in this case y corresponds to degrees Celsius.
To find b, plug in a known data point, say (F,C) = (32,0), and then solve for b:

0 = (5/9)*32 + b ----> b = -160/9. So C = (5/9)*F - (160/9) is the desired equation.

Note that we can solve for F in terms of C as well:

C + (160/9) = (5/9)F ---> F = (9/5)*C + (160/5) = (9/5)*C + 32.
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