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? answer attempt 2 out of 2 chirps per minute submit answer

Explanation:

Step1: Find the slope of the line of best fit

Use two points \((60,51)\) and \((64,52)\)
Slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{52 - 51}{64 - 60}=\frac{1}{4}=0.25\)

Step2: Use the point - slope form \(y - y_1=m(x - x_1)\)

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

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

\(57=0.25x + 36\)
Subtract 36 from both sides: \(57-36=0.25x\), so \(21 = 0.25x\)
Divide both sides by 0.25: \(x=\frac{21}{0.25}=84\)

Answer:

\(84\)