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 \((x_1,y_1)=(0,5)\) and \((x_2,y_2)=(9,8.5)\). Then \(m=\frac{8.5 - 5}{9 - 0}=\frac{3.5}{9}=\frac{35}{90}=\frac{7}{18}\).

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

We know that \(b\) is the \(y\) - intercept. From the point \((0,5)\), when \(x = 0\), \(y=5\), so \(b = 5\).
Substitute \(m=\frac{7}{18}\) and \(b = 5\) into \(y=mx + b\), we get \(y=\frac{7}{18}x+5\).

Answer:

\(y=\frac{7}{18}x + 5\)