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 64°f?

Explanation:

Step1: Identify line points

We use two clear points on the line of best fit: $(x_1,y_1)=(93,61)$ and $(x_2,y_2)=(90,60)$.

Step2: Calculate slope

Compute the slope $m$ of the line.
$m=\frac{y_2-y_1}{x_2-x_1}=\frac{60-61}{90-93}=\frac{-1}{-3}=\frac{1}{3}$

Step3: Find line equation

Use point-slope form $y-y_1=m(x-x_1)$ with $(93,61)$.
$y-61=\frac{1}{3}(x-93)$
Simplify to slope-intercept form:
$y=\frac{1}{3}x - 31 + 61$
$y=\frac{1}{3}x + 30$

Step4: Substitute temperature $y=64$

We need to find $x$ (chirps per minute) when $y=64$ (temperature).
$64=\frac{1}{3}x + 30$

Step5: Solve for $x$

Subtract 30 from both sides:
$64-30=\frac{1}{3}x$
$34=\frac{1}{3}x$
Multiply both sides by 3:
$x=34\times3=102$

Answer:

102