Answer:
or
or equivalently:
or
Step-by-step explanation:
To express the Fahrenheit temperature <em>as a linear function of the Celsius temperature</em>, F(c), we can proceed as follows.
We can use here <em>the two-point form</em> <em>equation</em> of a line:
[1]
We are asked to express the <em>Fahrenheit temperature</em> as a function of <em>Celsius temperature</em>, so the independent variable, in this case, is <em>x</em> (Celsius temperature) and the dependent variable is <em>y</em> (Fahrenheit temperature).
When temperature is zero degree Celsius (
), the Fahrenheit temperature is 32 (
).
When the Celsius temperature is 100 (
), the corresponding Fahrenheit temperature is 212 (
).
Then, using [1], we have:
![\\ y-32 = \frac{212 - 32}{100 - 0}(x-0)](https://tex.z-dn.net/?f=%5C%5C%20y-32%20%3D%20%5Cfrac%7B212%20-%2032%7D%7B100%20-%200%7D%28x-0%29)
![\\ y-32 = \frac{180}{100}(x)](https://tex.z-dn.net/?f=%5C%5C%20y-32%20%3D%20%5Cfrac%7B180%7D%7B100%7D%28x%29)
.
It could be also be written as:
=
, as it commonly appears in books.
Then <em>the Fahrenheit temperature express as a linear function of the Celsius temperature, F(c</em>) is ( solving the equation for <em>y </em>) :
or
.
Or equivalently:
or
We can check this using the given values from the question:
For 0 Celsius degrees, the Fahrenheit temperature is:
= 32 Fahrenheit degrees.
For 100 Celsius degrees, the Fahrenheit temperature is:
= 212 Fahrenheit degrees.