Question

a researcher studied the relationship between the number of times a certain species of crickets 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 crickets were measured to chirp 96 times in one minute?

Explanation:

Step1: Find the slope of the line

Use two points \((60,40)\) and \((72,50)\) on the line. The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
\(m=\frac{50 - 40}{72 - 60}=\frac{10}{12}=\frac{5}{6}\)

Step2: Find the equation of the line

Use the point - slope form \(y - y_1=m(x - x_1)\), take the point \((60,40)\)
\(y - 40=\frac{5}{6}(x - 60)\)
\(y - 40=\frac{5}{6}x-50\)
\(y=\frac{5}{6}x - 10\)

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

\(y=\frac{5}{6}\times96-10\)
\(y = 80 - 10\)
\(y = 70\)

Answer:

\(70\) degrees Fahrenheit