The outside temperature can be estimated based on how fast crickets chirp. At 104 chirps per minute, the temperature is 63 degreeree F At 176 chirps per minute, the temperature is 81 degreeree F. Using this information you can make a formula that relates chirp rate to temperature. Assume the relationship is linear, that is, the points form a straight line when plotted on a graph. What is the temperature if you hear 124 chirps per minute? What is the temperature if you hear 68 chirps per minute?

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franciscocruz28 franciscocruz28 · Answer 1 · 2020-01-21T15:23:33+01:00

Answer:

For 124 chirps per minute the temperature is 68 ºF.

For 68 chirps per minute the temperature is 54 ºF.

Step-by-step explanation:

Linear functions are those whose graph is a straight line. A linear function has the following form

[tex]f(x)=b+mx[/tex]

b is the constant term or the y intercept. It is the value of the dependent variable when x = 0.

m is the coefficient of the independent variable. It is also known as the slope and gives the rate of change of the dependent variable.

We know that

This information can be converted to Cartesian coordinates (x, y). Where x = the number of chirps per minute and y = the temperature in ºF.

To find a linear function that let us find the outside temperature from how fast crickets chirp we must:

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{81-63}{176-104}=\frac{1}{4}[/tex]

[tex]81=\frac{1}{4}\cdot 104+b[/tex]

Solving for b

[tex]b=81-\frac{1}{4} (176)=37[/tex]

Therefore, the linear function is

[tex]y=\frac{1}{4} \cdot x+37[/tex]

Now, using this linear function we can know the temperature when we know the chirps per minute:

For 124 chirps per minute the temperature is:

[tex]y=\frac{1}{4} \cdot (124)+37=68[/tex]

For 68 chirps per minute the temperature is:

[tex]y=\frac{1}{4} \cdot (68)+37=54[/tex]