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.

1 thought on “Ex: Write a Linear Equation that Models Cricket Chirps (Linear Equation Application)

  1. Nice Work! :). I understand everything and examples made in watching it one time. And I am able to do my work easily. Love it. Keep it up!

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