Answer
( a.) T=$\frac{1}{6}$ N +$\frac{307}{6}$
( b.) The slope of the equation is $\frac{1}{6}$. The slope represents a $\frac{1}{6}$ change in degrees Fahrenheit for every chirp per minute change.
( c.) 76 degrees Fahrenheit
Work Step by Step
( a.) Using the two sets of data given, 113 chirps per minute at 70 degrees Fahrenheit and 173 chirps per minute at 80 degrees Fahrenheit, calculate slope using the change in y over the change in x. Slope = $\frac{80-70}{173-113}$ = $\frac{1}{6}$. Next you find the equation using the equation y = mx+ b, solving for b.
70=$\frac{1}{6}$(113) + b.
b=$\frac{307}{6}$
The finished equation is T= $\frac{1}{6}$N + $\frac{307}{6}$
( b.) Slope is calculated by using the change of temperature over the change in chirps per minute, Slope = $\frac{80-70}{173-113}$ = $\frac{1}{6}$. Because of the way slope is found, you can rationalize that the change in Fahrenheit is proportionate to the change in chirps per minute.
( c.) Substitute 150 chirps per minute for the N variable.
T = $\frac{1}{6}$(150) + $\frac{307}{6}$
T= 76 degrees Fahrenheit
