Question

what is the equation of the trend line in the scatter plot? use the two yellow points to write the equation in slope - intercept form. write any coefficients as integers, proper fractions, or improper fractions in simplest form.

Explanation:

Step1: Find the slope \(m\)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(30,20)\) and \((x_2,y_2)=(70,60)\).

$$m=\frac{60 - 20}{70 - 30}=\frac{40}{40}=1$$

Step2: Use the slope - intercept form \(y = mx + b\)

Substitute \(m = 1\) and \((x,y)=(30,20)\) into \(y=mx + b\).

$$20=1\times30 + b$$

$$b=20 - 30=- 10$$

Step3: Write the equation

Substitute \(m = 1\) and \(b=-10\) into \(y = mx + b\).

$$y=x - 10$$

Answer:

\(y=x - 10\)