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 coordinates of the two blue points

The two blue points are \((2,1)\) and \((8,8)\)

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\)
Substitute \(x_1 = 2,y_1=1,x_2 = 8,y_2 = 8\)
\(m=\frac{8 - 1}{8 - 2}=\frac{7}{6}\)

Step3: Use the point - slope form \(y - y_1=m(x - x_1)\) and convert to slope - intercept form \(y=mx + b\)

Use the point \((2,1)\) and \(m=\frac{7}{6}\)
\(y - 1=\frac{7}{6}(x - 2)\)
\(y-1=\frac{7}{6}x-\frac{7}{3}\)
\(y=\frac{7}{6}x-\frac{7}{3}+1\)
\(y=\frac{7}{6}x-\frac{7}{3}+\frac{3}{3}\)
\(y=\frac{7}{6}x-\frac{4}{3}\)

Answer:

\(y = \frac{7}{6}x-\frac{4}{3}\)