Question

what is the equation of the trend line in the scatter plot?
use the two blue 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

The two blue points are \((4,6.5)\) and \((6,0)\).
The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substitute \(x_1 = 4,y_1=6.5,x_2 = 6,y_2 = 0\) into the formula:
\(m=\frac{0 - 6.5}{6 - 4}=\frac{-6.5}{2}=-\frac{13}{4}\)

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

We know \(m =-\frac{13}{4}\) and we can use the point \((6,0)\) to find \(b\).
Substitute \(x = 6,y = 0,m=-\frac{13}{4}\) into \(y=mx + b\):
\(0=-\frac{13}{4}\times6 + b\)
\(0=-\frac{78}{4}+b\)
\(b=\frac{78}{4}=\frac{39}{2}\)

Step3: Write the equation

The slope - intercept form is \(y=mx + b\).
Substitute \(m =-\frac{13}{4}\) and \(b=\frac{39}{2}\) into the formula:
\(y=-\frac{13}{4}x+\frac{39}{2}\)

Answer:

\(y =-\frac{13}{4}x+\frac{39}{2}\)