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 \(m\)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(3,0)\) and \((x_2,y_2)=(9,9)\). Then \(m=\frac{9 - 0}{9 - 3}=\frac{9}{6}=\frac{3}{2}\).

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

We know \(m=\frac{3}{2}\) and when \(x = 3,y = 0\). Substitute into \(y=mx + b\): \(0=\frac{3}{2}\times3 + b\). Solve for \(b\): \(b=-\frac{9}{2}\).

Step3: Write the equation

The slope - intercept form is \(y=\frac{3}{2}x-\frac{9}{2}\).

Answer:

\(y=\frac{3}{2}x-\frac{9}{2}\)