Question

a researcher studied the relationship between the number of times a certain species of cricket will chirp in one minute and the temperature outside. her data is expressed in the scatter plot and line of best fit below. based on the line of best fit, what temperature would it most likely be outside if this same species of cricket were measured to chirp 96 times in one minute?

Explanation:

Step1: Find the slope of the line of best fit

Use the formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(60,47)\) and \((x_2,y_2)=(72,50)\).
\(m=\frac{50 - 47}{72 - 60}=\frac{3}{12}=\frac{1}{4}\)

Step2: Find the equation of the line

Use the point - slope form \(y - y_1=m(x - x_1)\). Using the point \((60,47)\) and \(m = \frac{1}{4}\), we have \(y-47=\frac{1}{4}(x - 60)\).
Expand: \(y-47=\frac{1}{4}x-15\). Then \(y=\frac{1}{4}x + 32\)

Step3: Substitute \(x = 96\) into the equation

When \(x = 96\), \(y=\frac{1}{4}\times96+32\)
\(y = 24+32\)

Answer:

\(56\) degrees Fahrenheit