Question

what is the equation of the trend line in the scatter plot? use the two orange 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 \((x_1,y_1)=(3,7)\) and \((x_2,y_2)=(6,0)\).
\(m=\frac{0 - 7}{6 - 3}=\frac{-7}{3}\)

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

Substitute \(m =-\frac{7}{3}\) and the point \((x = 6,y = 0)\) into \(y=mx + b\).
\(0=-\frac{7}{3}\times6 + b\)
\(0=-14 + b\), so \(b = 14\)

Step3: Write the equation

The slope - intercept form is \(y=mx + b\). Substituting \(m =-\frac{7}{3}\) and \(b = 14\) gives \(y=-\frac{7}{3}x+14\)

Answer:

\(y =-\frac{7}{3}x + 14\)