Find a linear equation relating the number of chirps C to temperature in degrees T.

Question

At 10 degrees C a cricket chirped times per minute. At 20 degrees C the chirping increased to 112 chirps per minute.

Answer 1

We can think of temperature (T) like the x variable and the number of chirps (C) as the x variable. We will find and equation in the general slope-intercept form y = mx + b, where m is the slope of the line and b the y-intercept of the line. For our variables it will be C = mT + b.

 

The information given can be thought of as two ordered pairs (T,C): (10,40) and (20,112)

 

The first step is to calculate the slope, which is the difference in chirps divided by the difference in temperatures:

(112 - 40) / (20 - 10) = 72 / 10 = 36 / 5

 

Next we will select either one of our original ordered pairs and substitute the values for T, C, and our slope into the general equation. Let's select the first ordered pair simply because the numbers are smaller. 

40 = (36/5)(10) + b

40 = 72 + b             (do the math calculation)

-32 = b                   (subtract 72 from both sides)

 

Now we can write our equation since we have found the two pieces of information we needed, m and b.

C = (36/5)T - 32

 

(Alternatively, these last two steps could have been accomplished using the point-slope formula:

C - 40 = (36/5)(T - 10)

Then simplify the equation.)

 

To get the standard form of the equation,

clear the fraction by multiplying everything by 5:            5C = 36T - 160

then subtract 36T from both sides:                      -36T + 5C = -160

and conclude by multiplying by -1:                       36T  - 5C = 160