The table below resembles the table from the introduction to

The table below resembles the table from the introduction to this section. The rows of the table give us ordered pairs (C, F). Use any two of the ordered pairs from the table to derive the equation for F in terms of C. Use the equation from part a. to find the Fahrenheit temperature that corresponds to a Celsius temperature of 10degree. When it\'s 10 degreeC, it is degreeF.

Solution

a. Let F = aC + b where a,b are constants. We know that F = 32 when C = 0. On substituting these values of F and C in the equation, we get 32 = a*0 + c or, c = 32. Then the equation changes to F = aC + 32 . We also know that C = 25 when F = 77. On substituting these values of F and C in the equation, we get 77 = a (25) + 32 or, 25a = 77- 32 = 45. Therefore, a = 45/25 = 9/5. Then, the required equation is F = (9/5 )C + 32. or, F - 32 = 9/5 C. On multiplying both the sides by 1/9, we get C/5 = (F - 32)/ 9. We can verify this result by substituting other values of C and the given corresponding values of F from the given table.

b. On substituting C = 10 in the ewation, we get 10/5 =(F -32)/9 or, 2 = (F -32)/9 or, 18 = F - 32. Therefore F = 32+ 18 = 50. Thus the Farenheit temperature that corresponds to a Celcius rtemperature of 10⁰ is 50⁰ , or, when it is 10⁰C, it is 50⁰F