SOLUTION: A temperature of 10°C corresponds to a temperature of 50°F. Also 40°C corresponds to 104°F. Find the linear equation relating F and C.

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Question 100763: A temperature of 10°C corresponds to a temperature of 50°F. Also 40°C corresponds to 104°F. Find the linear equation relating F and C.
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
We are given:
10C+=+50F
40C+=+104F
We can assume we have a grid of C (the x-axis) and F (the y-axis).
So these correspondences can be viewed as xy pairs that define points in the plane: (10,50) and (40,104).
Finding the slope of the line, we have:

The general equation for a line is y = mx + b, so
y+=+%289%2F5%29x+%2B+b
And, looking back we notice that when x=10, y=50. So we can substitute:
50+=+%289%2F5%2910+%2B+b
50+=+18+%2B+b, so
b+=+32, which is the y-intercept.
Now the equation is
y+=+%289%2F5%29x+%2B+32, which is perhaps more familiar by substituting F for y (meaning degrees Farenheit) and C for x (meaning Celsius).
F+=+%289%2F5%29C+%2B+32.