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 slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(2,0)\) and \((x_2,y_2)=(6,6)\).
\(m=\frac{6 - 0}{6 - 2}=\frac{6}{4}=\frac{3}{2}\)

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

Use the slope - intercept form \(y = mx + b\) and substitute \(m=\frac{3}{2}\), \(x = 2\), \(y = 0\).
\(0=\frac{3}{2}\times2+b\)
\(0 = 3 + b\), so \(b=-3\)

Step3: Write the equation

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

Answer:

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