# The Celsius to Fahrenheit Conversion Problem ```The Celsius to Fahrenheit Conversion Problem
The freezing point of water is 0 degrees Celsius, which is 32 degrees
Fahrenheit. The boiling point is 100&deg; Celsius and 212&deg; Fahrenheit.
Let the x-axis represent &deg;C and the y-axis be &deg;F. On an xy-grid the freezing
point corresponds to the y-intercept (0, 32), and the boiling point is located
at (100, 212).
The slope m =
y2 − y1
of the line through these two points is:
x2 − x1
m=
y2 − y1 212 − 32 180 9
=
=
=
x2 − x1 100 − 0 100 5
Now, apply the Point-Slope form y − y1 = m( x − x1 ) of a linear equation:
9
( x − 0)
5
9
y = x + 32
5
y − 32 =
Checking that an x-value of 100 produces a y-value of 212:
y=
9
100
(100 ) + 32 = 9 ⎛⎜ ⎞⎟ + 32 = 9(20) + 32 = 180 + 32 = 212
5
⎝ 5 ⎠
The equation that calculates Fahrenheit degrees F from Celsius degrees C is:
9
F = C + 32
5
Solve this equation for C so obtain the Celsius from Fahrenheit conversion:
9
9
5
F = C + 32 ⇒ 9 F = F − 32 = C ⇒= 5 ( F − 32 ) = 9C ⇒ ( F − 32 ) = C
5
5
9
5
C = ( F − 32 )
9
```