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 formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(20,30)\) and \((x_2,y_2)=(70,70)\).
\(m=\frac{70 - 30}{70 - 20}=\frac{40}{50}=\frac{4}{5}\)

Step2: Find the y - intercept

Use the slope - intercept form \(y = mx + b\). Substitute \(m=\frac{4}{5}\), \(x = 20\), and \(y = 30\) into the equation.
\(30=\frac{4}{5}\times20+b\)
\(30 = 16 + b\)
\(b=30 - 16=14\)

Answer:

\(y=\frac{4}{5}x + 14\)