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 57°f?

Explanation:

Step1: Find the slope of the line of best fit

Use the formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Take two points on the line of best fit, say \((60,51)\) and \((64,52)\).
\(m=\frac{52 - 51}{64 - 60}=\frac{1}{4}= 0.25\)

Step2: Use the point - slope form \(y - y_1=m(x - x_1)\) to find the equation of the line

Using the point \((60,51)\) and \(m = 0.25\), the equation is \(y-51=0.25(x - 60)\)
Expand: \(y-51=0.25x-15\)
Simplify: \(y = 0.25x+36\)

Step3: Substitute \(x = 57\) into the equation

\(y=0.25\times57 + 36\)
\(y = 14.25+36\)
\(y=50.25\approx50\)

Answer:

50