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, how many times would the cricket most likely chirp per minute if the temperature outside were 68°f?

Explanation:

Step1: Find the slope of the line

Use the formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Take two points \((60,56)\) and \((70,59)\).
\(m=\frac{59 - 56}{70 - 60}=\frac{3}{10}=0.3\)

Step2: Find the equation of the line

Use the point - slope form \(y - y_1=m(x - x_1)\). Using the point \((60,56)\) and \(m = 0.3\), we get \(y-56=0.3(x - 60)\).
Expand: \(y-56=0.3x-18\).
Then \(y = 0.3x+38\)

Step3: Substitute \(x = 68\) into the equation

\(y=0.3\times68 + 38\)
\(y=20.4+38\)
\(y = 58.4\approx58\)

Answer:

\(58\)