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 coordinates of the two yellow points

The two yellow points are \((4,8)\) and \((8,4)\)

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\)
Substitute \((x_1,y_1)=(4,8)\) and \((x_2,y_2)=(8,4)\)
\(m=\frac{4 - 8}{8 - 4}=\frac{-4}{4}=- 1\)

Step3: Use the slope - intercept form \(y = mx + b\) to find \(b\)

Substitute \(m=-1\) and \((x,y)=(4,8)\) into \(y = mx + b\)
\(8=-1\times4 + b\)
\(8=-4 + b\)
Add \(4\) to both sides: \(b = 8 + 4=12\)

Step4: Write the equation of the line

The slope - intercept form is \(y=mx + b\), with \(m=-1\) and \(b = 12\)
So the equation is \(y=-x + 12\)

Answer:

\(y=-x + 12\)