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, what temperature would it most likely be outside if this same species of cricket were measured to chirp 120 times in one minute?

Explanation:

Step1: Find the slope - intercept form

First, find two points on the line of best - fit, say $(x_1,y_1)=(60,47)$ and $(x_2,y_2)=(90,55)$. The slope $m$ of the line is given by the formula $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{55 - 47}{90 - 60}=\frac{8}{30}=\frac{4}{15}$. Using the point - slope form $y - y_1=m(x - x_1)$ with the point $(60,47)$, we get $y-47=\frac{4}{15}(x - 60)$. Expanding, $y-47=\frac{4}{15}x-16$, so $y=\frac{4}{15}x + 31$.

Step2: Substitute the value of $x$

We are given that the number of chirps per minute $x = 120$. Substitute $x = 120$ into the equation $y=\frac{4}{15}x+31$. Then $y=\frac{4}{15}\times120 + 31$. Calculate $\frac{4}{15}\times120=32$. So $y=32 + 31=63$.

Answer:

63