Question

According to wildlife experts, the rate at which crickets chirp per minute is a function of the temperature in degrees Fahrenheit. James observed that when the temp was 60 degrees, there were 84 chirps and when the temp was 85 degrees, there were 184 chirps. Write a linear function to model the relationship between the number of chirps and the temperature.

Answer 1

Explanation:

We will let the x coordinates be the temp and the y coordinates by the number of chirps. Our coordinates then will look like this:

(60, 84) and (85, 184). If this is linear, then first we will find the slope of the line which will tell us, in the context of this problem, how many chirps a cricket gives per 1 degree of temp increase.

The slope formula is:

`m=(y_2-y_1)/(x_2-x_1)` and filling in our numbers:

`m=(184-84)/(85-60)=(100)/(25)= 4`

This means that for every 1 degree temp increase, a cricket will give 4 chirps. That's the m value in y = mx + b. Now we will pick one of the coordinates, doesn't matter which one, and use those x and y values in the point-slope form of a line to get the equation. I will choose (60, 85), just because. Using the other point will give you the exact same line equation, I PROMISE!

Using 85 as y1 and 60 as x1 in

y - y1 = m(x - x1) gives us

y - 85 = 4(x - 60) and

y - 85 = 4x - 240 and

y = 4x - 240 + 85 and

y = 4x - 155