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 \((x_1,y_1)=(1,0)\) and \((x_2,y_2)=(8,9)\).

$$m=\frac{9 - 0}{8 - 1}=\frac{9}{7}$$

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

We know \(m=\frac{9}{7}\) and when \(x = 1,y = 0\). Substitute into \(y=mx + b\):

$$0=\frac{9}{7}(1)+b$$

$$b=-\frac{9}{7}$$

Step3: Write the equation

Substitute \(m=\frac{9}{7}\) and \(b =-\frac{9}{7}\) into \(y=mx + b\)

$$y=\frac{9}{7}x-\frac{9}{7}$$

Answer:

\(y=\frac{9}{7}x-\frac{9}{7}\)