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 84 times in one minute?

Explanation:

Step1: Find the slope of the line

The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using points $(60,53)$ and $(64,54)$:
$m=\frac{54 - 53}{64 - 60}=\frac{1}{4}= 0.25$

Step2: Find the y - intercept

Using the point - slope form $y - y_1=m(x - x_1)$ with point $(60,53)$ and $m = 0.25$.
$y-53=0.25(x - 60)$
$y-53=0.25x-15$
$y=0.25x + 38$

Step3: Make a prediction

Substitute $x = 84$ into the equation $y=0.25x + 38$.
$y=0.25\times84+38$
$y = 21+38$
$y = 59$

Answer:

$59$