a researcher studied the relationship between the number of times a certain species of cricket will chirp in…

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

Explanation:

Step1: Find the slope of the line

We use two - point formula for slope $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points on the line $(60,51)$ and $(64,52)$. Then $m=\frac{52 - 51}{64 - 60}=\frac{1}{4}=0.25$.

Step2: Find the y - intercept

Using the point - slope form $y - y_1=m(x - x_1)$ with the point $(60,51)$ and $m = 0.25$, we have $y-51 = 0.25(x - 60)$. Expanding gives $y-51=0.25x-15$, so $y = 0.25x+36$.

Step3: Substitute the temperature value

We want to find $x$ when $y = 57$. Substitute $y = 57$ into the equation $57=0.25x + 36$.

Step4: Solve for x

First, subtract 36 from both sides: $57-36=0.25x$, so $21 = 0.25x$. Then divide both sides by 0.25: $x=\frac{21}{0.25}=84$.