write an equation that represents the current tempertaure based on the cricket chips. define your variables.

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.  

Answer 1

The standard linear equation is:

mx + b = y

 

So here's what we know:

68x + b = 124

80x + b = 172

 

If we invert the first equation, we can get rid of b and thus isolate x:

 80x + b = 172

-68x - b = -124

12x = 48

x = 12

 

Now that we have x, we can solve for b:

68 * 4 + b = 124

272 + b = 124

b = -148

 

Let's check our answer:

80*4 - 148 = 172

320 - 148 = 172

172 = 172

 

So our final equation is:

4 * Temp - 148 = chirps