# Ex: Write a Linear Equation that Models Cricket Chirps (Linear Equation Application)

The number of chirps per minute, C, that the tree cricket

makes is linearly dependent on the temperature, T, in Fahrenheit. The crickets do not chirp

at all at 40 degrees and at 50 degrees they chirp

about 42 times per minute. Part A, we’re asked to express

the number of chirps, C, in terms of the temperature, T. To find the equation that relates C and T, we’ll write the given

information as ordered pairs, then use the ordered pairs

to find the linear equation. Because we want to

express C in terms of T, T is the input variable and

C is the output variable and therefore each ordered pair will be in the form of T comma C. Where, again, T is the

temperature in Fahrenheit and C is the number of chirps per minute. So going back to the given information, the crickets do not chirp

at all at 40 degrees. This would be the ordered

pair, 40 comma zero, again because the first

value is the temperature, the second value is the

number of chirps per minute. Then we’re also told, at 50 degrees, they chirp

42 times per minute, which would be the

ordered pair 50 comma 42. A linear equation and slope intercept form is in the form Y equals M X plus B, where X is the input variable

and Y is the output variable. But because we’re writing C in terms of T, our equation is going to be in the form of C equals M T plus B. So if we can determine M, the slope, and B, the vertical intercept, we’ll have our equation

of C in terms of T. We know how to find the

slop given two points. Use this formula here, where the slope M is

equal to the change of Y, which in this case

would be the change of C divided the change of X, which in this case would

be the change in T. So to keep things organized, let’s call this ordered pair

T sub one comma C sub one, this ordered pair T sub

two comma C sub two. So C sub two minus C sub

one is 42 minus zero. T sub two minus T sub one is 50 minus 40. Simplifying, we get 42 divided by 10, which equals 4.2. So now because we know

the slope is equal to 4.2, we’ll substitute 4.2

for M in our equation. So now we know that C must equal 4.2 times T plus B. To find the value of B, we’ll use one of the ordered

pairs and perform substitution for T and C, and then solve for B. Let’s go and use this

first ordered pair here. So we’ll substitute

zero for C and 40 for T. So this’ll give us the equation zero equals 4.2 times 40 plus B. So we have zero equals

4.2 times 40 equals 168. So we have zero equals 168 plus B, solving for B, we

subtract 168 on both sides and we have B equals negative 168. And now we’ll substitute this

value for B into our equation. Which’ll give us the equation

C equals 4.2 T minus 168. So this is the equation

we need for part A. Notice C equals is already here, so we only enter 4.2 T minus 168. Now for part B, we’re asked to determine how many chirps per minute will the crickets make at 60 degrees? So using our equation we

want to find the value of C when T equals 60. So we’d have C of 60 which equals 4.2 times 60 minus 168. Let’s go ahead and find

this function value on the calculator. So we have 4.2, times 60, minus 168. Enter, and this gives us 84. Remember C is number of chirps per minute. So looking at part B, our answer is 84, and the units which we select here, again, is chirps per minute. I hope you found this helpful.

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