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 slope

The two blue points are \((5,0)\) and \((8,6)\).
The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substitute \(x_1 = 5,y_1=0,x_2 = 8,y_2 = 6\) into the formula:
\(m=\frac{6-0}{8 - 5}=\frac{6}{3}=2\)

Step2: Find the y - intercept

Use the slope - intercept form \(y=mx + b\).
We know \(m = 2\) and the point \((5,0)\) (we can also use \((8,6)\)). Substitute \(x = 5,y = 0,m=2\) into \(y=mx + b\):
\(0=2\times5+b\)
\(0 = 10 + b\)
Solve for \(b\): \(b=- 10\)

Step3: Write the equation

Substitute \(m = 2\) and \(b=-10\) into \(y=mx + b\)
\(y = 2x-10\)

Answer:

\(y = 2x-10\)