Question

A researcher studied the relationship between the number of times a certain speciesof cricket will chirp in one minute and the temperature outside. Her data is expressedin the scatter plot and line of best fit below. Based on the line of best fit, whattemperature would it most likely be outside if this same species of cricket weremeasured to chirp 96 times in one minute?Answer: _____°F

Answer 1

To answer the question we need to find the equation of the line, this is given by:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Using the points given we have:

$\begin{gathered} y-62=\frac{63-62}{93-90}(x-90) \\ y-62=\frac{1}{3}(x-90) \\ y=\frac{1}{3}x-30+62 \\ y=\frac{1}{3}x+32 \end{gathered}$

Then we have to remeber that x represents the number of chirps and y the temperature. If we have 96 chirps (that is x=96), then:

$\begin{gathered} y=\frac{1}{3}\cdot96+32 \\ y=32+32 \\ y=64 \end{gathered}$

Therefore the temperature is likely to be 64° F.