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 116 times in one minute?

Question

Accepted Answer

# Explanation:
## Step1: Find the slope of the line of best fit
The formula for slope $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using the points $(100,63)$ and $(104,64)$, we have $m=\frac{64 - 63}{104 - 100}=\frac{1}{4}=0.25$

## Step2: Use the point - slope form $y - y_1=m(x - x_1)$
Using the point $(100,63)$ and $m = 0.25$, the equation of the line is $y-63=0.25(x - 100)$

## Step3: Simplify the equation
$$
\begin{align*}
y-63&=0.25x-25\
y&=0.25x + 38
\end{align*}
$$

## Step4: Substitute $x = 116$ into the equation
When $x = 116$, $y=0.25\times116+38$
$$
\begin{align*}
y&=29 + 38\
y&=67
\end{align*}
$$

# Answer:
$67$ degrees Fahrenheit

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QUESTION IMAGE

Question

Explanation:

Step1: Find the slope of the line of best fit

Step2: Use the point - slope form \(y - y_1=m(x - x_1)\)

Step3: Simplify the equation

Step4: Substitute \(x = 116\) into the equation

Answer: