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?
(scatter plot with x - axis: chirps per minute, y - axis: temperature (degrees fahrenheit), line of best fit with points (60,55), (75,59), (90,63), (105,67))

Explanation:

Step1: Find line slope using points

Use points $(60,55)$ and $(90,63)$:
$$m=\frac{63-55}{90-60}=\frac{8}{30}=\frac{4}{15}$$

Step2: Find y-intercept of line

Use point $(60,55)$ in $y=mx+b$:
$$55=\frac{4}{15}(60)+b \implies 55=16+b \implies b=39$$

Step3: Define line equation

$$y=\frac{4}{15}x+39$$

Step4: Substitute x=120 into equation

$$y=\frac{4}{15}(120)+39=32+39$$

Answer:

71 degrees Fahrenheit