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 \((x_1,y_1)=(5,2.8)\) and \((x_2,y_2)=(8,5.6)\) (approximate values of the yellow points). Then \(m=\frac{5.6 - 2.8}{8 - 5}=\frac{2.8}{3}=\frac{14}{15}\approx\frac{1}{2}\) (by visual - estimation, if we assume more integer - like points for simplicity, say \((5,3)\) and \((8,6)\)). Using \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{6 - 3}{8 - 5}=1\)

Step2: Use the point - slope form \(y - y_1=m(x - x_1)\)

Using the point \((5,3)\) and \(m = 1\), \(y-3=1\times(x - 5)\)

Step3: Convert to slope - intercept form \(y=mx + b\)

Expand \(y-3=x - 5\), then \(y=x-5 + 3\)

Answer:

\(y=x - 2\)