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 61°f?

Explanation:

Step1: Find the slope of the line of best fit

We have two points on the line: \((100, 59)\) and \((104, 60)\). The slope \(m\) is calculated as \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{60 - 59}{104 - 100}=\frac{1}{4}=0.25\).

Step2: Find the equation of the line

Using the point - slope form \(y - y_1=m(x - x_1)\) with the point \((100, 59)\) and \(m = 0.25\), we get \(y-59 = 0.25(x - 100)\). Simplifying, \(y-59=0.25x - 25\), so \(y=0.25x + 34\).

Step3: Predict the number of chirps at \(y = 61\)

We know that \(y\) is the temperature (in Fahrenheit) and \(x\) is the number of chirps. We want to find \(x\) when \(y = 61\). Substitute \(y = 61\) into the equation \(61=0.25x + 34\). Subtract 34 from both sides: \(61 - 34=0.25x\), so \(27 = 0.25x\). Then \(x=\frac{27}{0.25}=108\). Or we can use the slope - intercept interpretation. From the two points, when \(y\) increases by 1 (from 59 to 60), \(x\) increases by 4 (from 100 to 104). We need to find \(x\) when \(y\) goes from 59 to 61 (an increase of 2). So the increase in \(x\) is \(2\times4 = 8\). So \(x=100 + 8=108\).

Answer:

108