SOLUTION: The outside temperature can be estimated based on how fast crickets chirp. At 104 chirps per minute, the temperature is 63 °F. At 176 chirps per minute, the temperatur

Algebra ->  Linear-equations -> SOLUTION: The outside temperature can be estimated based on how fast crickets chirp. At 104 chirps per minute, the temperature is 63 °F. At 176 chirps per minute, the temperatur      Log On


   

Question 1151187: The outside temperature can be estimated based on how fast crickets chirp.
At 104 chirps per minute, the temperature is
63
°F.
At 176 chirps per minute, the temperature is
81
°F.
Using this information, you can make a formula that relates chirp rate to temperature. Assume the relationship is linear, that is the points form a straight line when plotted on a graph.
What is the temperature if you hear
148
chirps per minute?
What is the temperature if you hear
84
chirps per minute?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let the number of chirps be x and the number of degrees y
At 104 chirps per minute, the temperature is 63°F. we have
x=104 and y=63
that is a point (104 , 63) on a line
At 176 chirps per minute, the temperature is 81°F.
that is a point (176 , 81) on a line
the equation of a line is:
y=mx%2Bb where m is a slope and b is y-intercept
using given points find slope m:
m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
m=%2881-63%29%2F%28176-104%29
m=18%2F72.....simplify, divide both numerator and denominator by 18
m=1%2F4
y=%281%2F4%29x%2Bb .......now use one point to find b
63=%281%2F4%29104%2Bb
63=26%2Bb
63-26=b
b=37
your equation is:
y=%281%2F4%29x%2B37


What is the temperature if you hear 148 chirps per minute?
given: x=148
y=%281%2F4%29148%2B37
y=37%2B37
y=74=> the temperature is 74°F

What is the temperature if you hear 84+chirps per minute?
given: x=84
y=%281%2F4%2984%2B37
y=21%2B37
y=58=> the temperature is 58°F