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 \((x_1,y_1)=(3,8)\) and \((x_2,y_2)=(7,3)\).
\(m=\frac{3 - 8}{7 - 3}=\frac{-5}{4}\)

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

Substitute \(m =-\frac{5}{4}\), \(x = 3\), and \(y = 8\) into \(y=mx + b\).
\(8=-\frac{5}{4}(3)+b\)
\(8=-\frac{15}{4}+b\)
\(b = 8+\frac{15}{4}=\frac{32 + 15}{4}=\frac{47}{4}\)

Step3: Write the equation

The slope - intercept form is \(y=mx + b\). Substitute \(m =-\frac{5}{4}\) and \(b=\frac{47}{4}\)
\(y=-\frac{5}{4}x+\frac{47}{4}\)

Answer:

\(y =-\frac{5}{4}x+\frac{47}{4}\)