Question

1. the scatter plot shows the relationship between the number of times a cricket chirps and the current temperature. write an equation for the line of fit. then use it to make a conjecture about the temperature when there are 40 cricket chirps. (example 2) cricket chirps temperature (°f) chirps in 14 seconds

Explanation:

Step1: Identify two points on line

Choose (0, 25) and (40, 60) from the line of fit.

Step2: Calculate slope of the line

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{60-25}{40-0}=\frac{35}{40}=\frac{7}{8}=0.875$

Step3: Write line equation (slope-intercept)

Use $y=mx+b$, $b=25$ (y-intercept)
$y=0.875x + 25$

Step4: Substitute x=40 into equation

$y=0.875(40) + 25$
$y=35 + 25=60$

Answer:

Equation of the line of fit: $y = \frac{7}{8}x + 25$ or $y=0.875x+25$
Temperature at 40 chirps: $60^\circ\text{F}$