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 63°f? answer attempt 1 out of 2 chirps per minute submit answer

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 \((x_2,y_2)=(90,55)\).

$$m=\frac{55 - 47}{90 - 60}=\frac{8}{30}=\frac{4}{15}$$

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

Using \((x_1,y_1)=(60,47)\) and \(m = \frac{4}{15}\), we have \(y-47=\frac{4}{15}(x - 60)\).

$$y-47=\frac{4}{15}x-16$$

$$y=\frac{4}{15}x + 31$$

Step3: Substitute \(y = 63\) (temperature) into the equation and solve for \(x\) (chirps)

$$63=\frac{4}{15}x+31$$

$$63 - 31=\frac{4}{15}x$$

$$32=\frac{4}{15}x$$

$$x=\frac{32\times15}{4}=120$$

Answer:

\(120\)