Question

what is the equation of the trend line in the scatter plot?
use the two yellow 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 \((x_1,y_1)=(0,2)\) and \((x_2,y_2)=(6,7)\).

$$m=\frac{7 - 2}{6 - 0}=\frac{5}{6}$$

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

The slope - intercept form is \(y=mx + b\), where \(b\) is the \(y\) - intercept. From the point \((0,2)\), when \(x = 0\), \(y=2\), so \(b = 2\).
Substitute \(m=\frac{5}{6}\) and \(b = 2\) into \(y=mx + b\).

$$y=\frac{5}{6}x+2$$

Answer:

\(y=\frac{5}{6}x + 2\)