How do you convert degrees C to degrees F?

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Answer 1 · 2016-11-17T17:42:36

Please see the explanation for the derivation of:

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

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

$y = m x + b$ $y = mx + b$

Make the y coordinate the Fahrenheit value, F:

$F = m (x) + b$ $F = m(x) + b$

Make the x coordinate the Celsius value, C:

$F = m (C) + b$ $F = m(C) + b$

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

$32 = m (0) + b$ $32 = m(0) + b$

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

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

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

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

$180 = m (100)$ $180 = m(100)$

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

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