Question

what is the equation of the trend line in the scatter plot?
use the two orange 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 \((x_1,y_1)=(0,8)\) and \((x_2,y_2)=(9,2)\).

$$m=\frac{2 - 8}{9 - 0}=\frac{-6}{9}=-\frac{2}{3}$$

Step2: Find the \(y\) - intercept \(b\)

The slope - intercept form is \(y = mx + b\). Using the point \((x = 0,y = 8)\), when \(x = 0\), \(y=b\). So \(b = 8\).

Step3: Write the equation

Substitute \(m=-\frac{2}{3}\) and \(b = 8\) into \(y=mx + b\).

$$y=-\frac{2}{3}x + 8$$

Answer:

\(y =-\frac{2}{3}x + 8\)