SOLUTION: On a certain day, the temperature was 37 Fahrenheit at 10am and 49 fahrenheit at 1pm. if the temperature rose at a constant rate from 10am to 1pm on that day, what was the temperat

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Question 969646: On a certain day, the temperature was 37 Fahrenheit at 10am and 49 fahrenheit at 1pm. if the temperature rose at a constant rate from 10am to 1pm on that day, what was the temperature at 11am?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
(t,F) points.
If 10AM is time t=0, then points (0,37) and (3, 49). The first point serves as a vertical axis intercept.

F=m%2At%2B37
F=%28%2849-37%29%2F%283-0%29%29t%2B37
highlight%28F=%284%2F3%29t%2B37%29, t=0 corresponds to 10AM.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
On a certain day, the temperature was 37 Fahrenheit at 10am and 49 fahrenheit at 1pm. if the temperature rose at a constant rate from 10am to 1pm on that day, what was the temperature at 11am?
Let x be time, with starting time being x = 0. Then y is the temperature at a particular time of the day
We then get: f%28x%29+=+mx+%2B+b
Points: (0, 37) and (3, 49)
Slope or m = %2837+-+49%29%2F%280+-+3%29, or m = 4
y+-+y%5B1%5D+=+m%28x+-+x%5B1%5D%29
y+-+37+=+4%28x+-+0%29
y+-+37+=+4x

y+=+4x+%2B+37, or f%28x%29+=+4x+%2B+37 -------- Equation representing temperature at a certain time of the day
Since 11am is the 1st hour, or hour 1 after 10am, then f%28x%29+=+4x+%2B+37 becomes: f%281%29+=+4%281%29+%2B+37, or f%281%29+=+4+%2B+37.
Therefore, temperature, 1 hour after 10am, or at 11am = highlight_green%2841%5Eo%29