Question

Biologists have found that the number of chirps some crickets make per minute is related to temperature. the relationship is very close to being linear. When crickets chirp 124 times a minute, it is about 68 degrees Fahrenheit. When they chirp 172 times a minute, it is about 80 degrees Fahrenheit.
Identify the variables
x= ___________
y= ___________

y-intercept= __________
slope= _______

Create an equation in y=mx+b form

How warm is it when the crickets are chirping 150 times a minute?

Please help, I have to turn this in tomorrow

45 POINTS​

Answer 1

Answer:

It is $74.24$ degrees Fahrenheit when the crickets are chirping $150$ times a minute.

Variables $x = Chirps$ and  $y = Degrees$

y-intercept $= 38.24$

slope $= 0.24$

Step-by-step explanation:

As the chirps are $124$ times per minute for $68$ degrees Fahrenheit we will consider it in $(x_1,y_1) = (124,68)$.

Now when the chirps are $172$ times and temperature is $80$ degrees we consider it $(x_2,y_2) = (172,80)$.

To find the slope we can use point-slope formula.

Where $m$ is the slope and $m=\frac{y_2-y_1}{x_2-x_1} =\frac{80-68}{172-124}= 0.24$

To find y-intercept we will plug out the value of slope in $y=m(x)+b$ choosing point $(x_1,y_1) = (124,68)$.

So $b=y-m(x) =68-124(0.24) =68-29.76=38.24$

And the equation is $y=0.24(x)+b$

To calculate temperature for $150$ chirpings we have to plug $x=150$ and $b=38.24$ in our above equation which is in form of $y=m(x)+b$

$y=0.24(x)+b$

$y=0.24(150)+38.24=74.24\approx 75$ degrees Fahrenheit.

Finally we have :

Temperature $74.24$ degrees Fahrenheit.

With variables $x = Chirps$ and  $y = Degrees$

y-intercept $= 38.24$ and

slope $= 0.24$