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 \((3,1)\) and \((9,9)\).
The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substitute \(x_1 = 3,y_1 = 1,x_2=9,y_2 = 9\) into the formula:
\(m=\frac{9 - 1}{9 - 3}=\frac{8}{6}=\frac{4}{3}\)

Step2: Find the y - intercept

Use the slope - intercept form \(y=mx + b\). Substitute \(m=\frac{4}{3}\) and the point \((3,1)\) into the equation.
\(1=\frac{4}{3}\times3 + b\)
\(1 = 4 + b\)
Solve for \(b\): \(b=1 - 4=-3\)

Step3: Write the equation

The slope - intercept form is \(y = mx + b\). Substitute \(m=\frac{4}{3}\) and \(b=-3\)
\(y=\frac{4}{3}x-3\)

Answer:

\(y=\frac{4}{3}x - 3\)