A temperature of 30 degrees F is equivalent to 271.89 degrees K, while a temperature of 94 degrees F is equivalent to 307.44 degrees K. Find the equation converting Kelvin temperature to Fahrenheit. What is the Fahrenheit temperature when it is 212 degrees K?
Algebra - MathMate, Sunday, June 3, 2012 at 8:00am
Assume a linear relationship of:
where m=slope, and b=intercept.
We have two given points, (271.89,30) and (307.44,94)
The standard formula for m (slope) is:
With m=1.8, substitute one of the points into equation (1) to find b:
So the conversion equation is:
I leave it to you to substitute K=212 in order to find the fahrenheit degrees.
Algebra - Reiny, Sunday, June 3, 2012 at 8:02am
Let F = aK + b , (treating it like the linear equation y = mx + b)
we have two points (271.89, 30) and (307.44, 94)
a = slope = (94-30)/(307.44 - 271.89) = 64/35.55
let's go with 1.8
so F = 1.8K + b
sub in (271.89,30) to find b
30 = 1.8(271.89) + b
b = -459.48
F = 1.8K - 459.48
so when K = 212
F = 1.8(212) - 459.48 = -77.9° Fahrenheit
To MathMate - Algebra - Reiny, Sunday, June 3, 2012 at 8:04am
What's that saying again, some kind of minds thinking alike ?? lol
Algebra - MathMate, Sunday, June 3, 2012 at 8:07am
Great minds think alike! haha!