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 \((x_1,y_1)=(0,8)\) and \((x_2,y_2)=(5,3)\).

$$m=\frac{3 - 8}{5-0}=\frac{-5}{5}=- 1$$

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

The slope - intercept form of a line is \(y = mx + b\). When \(x = 0\), from the point \((0,8)\), we can see that \(b = 8\) (since when \(x = 0\), \(y=b\) in the equation \(y=mx + b\)).

Step3: Write the equation

Substitute \(m=-1\) and \(b = 8\) into the slope - intercept form \(y=mx + b\).
The equation is \(y=-x + 8\)

Answer:

\(y=-x + 8\)