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 \((x_1,y_1)=(3,1)\) and \((x_2,y_2)=(8,6)\).
\(m=\frac{6 - 1}{8 - 3}=\frac{5}{5}=1\)

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

Use the slope - intercept form \(y = mx + b\). Substitute \(m = 1\) and \((x,y)=(3,1)\) into \(y=mx + b\).
\(1=1\times3 + b\)
\(b=1 - 3=- 2\)

Step3: Write the equation

Substitute \(m = 1\) and \(b=-2\) into \(y=mx + b\).
\(y=x - 2\)

Answer:

\(y=x - 2\)