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