Question 55831
<pre><font size = 4><b>o.k., one more for today, thank you everyone who helped me! 
A temperature of 41 degrees F is equivalent to 278.2 degrees K,
while a temp. of 86 degrees F is equivalent to 303.2 degrees K. 
Find the converting Kelvin temp. to Fahrenheit. What is the 
Fahrenheit temp. when it is 180 degrees K? 
Word problems stump me....

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This is the problem of finding the equation of the line that
passes through two points.

Let x = Kelvin temperature
Let y = Fahrenheit temperature

>>...41 degrees F is equivalent to 278.2 degrees K...<<

Translation: when x = 278.2, y = 41 OR

The line passes through the point (278.2, 41)

>>...56 degrees F is equivalent to 303.2 degrees K...<<

Translation: when x = 303.2, y = 86 OR

The line passes through the point (303.2, 86)

Use the slope formula

     y<sub>2</sub> - y<sub>1</sub>        86 - 41       9   
m = --------- = --------------- = -- = 1.8
     x<sub>2</sub> - x<sub>1</sub>     303.2 - 278.2    5     

Use the point-slope formula

y - y<sub>1</sub> = m(x - x<sub>1</sub>)

y - 41 = 1.8(x - 278.2)

y - 41 = 1.8x - 500.76

     y = 1.8x - 459.76

We can change the x to K and the y to F:

     F = 1.5K - 459.76

>>...What is the Fahrenheit temp. when it is 180 degrees K?...<<

     F = 1.5(180) - 459.76

     F = -135.76°

Edwin</pre>