# How do you convert degrees C to degrees F?

Nov 17, 2016

Please see the explanation for the derivation of:

$F = \frac{9}{5} \left(C\right) + 32 {F}^{\circ}$

#### Explanation:

You can actually derive the equation, using the slope-intercept form of the equation of a line and two known points:

$y = m x + b$

Make the y coordinate the Fahrenheit value, F:

$F = m \left(x\right) + b$

Make the x coordinate the Celsius value, C:

$F = m \left(C\right) + b$

You can find the value of "b" by using the freezing point at $0 {C}^{\circ}$ and $32 {F}^{\circ}$

$32 = m \left(0\right) + b$

$b = 32 {F}^{\circ}$

$F = m \left(C\right) + 32 {F}^{\circ}$

You and find the value of "m" by using the boiling point of water at $100 {C}^{\circ}$ and $212 {F}^{\circ}$

$212 = m \left(100\right) + 32 {F}^{\circ}$

$180 = m \left(100\right)$

$m = \frac{180}{100} = \frac{9}{5}$

$F = \frac{9}{5} \left(C\right) + 32 {F}^{\circ}$