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 \((2,1)\) and \((7,6)\).
The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substitute \(x_1 = 2,y_1=1,x_2 = 7,y_2 = 6\) into the formula:
\(m=\frac{6 - 1}{7 - 2}=\frac{5}{5}=1\)

Step2: Find the y - intercept

Use the slope - intercept form \(y=mx + b\), substitute \(m = 1\) and the point \((2,1)\) (we can also use \((7,6)\)) into it.
\(1=1\times2 + b\)
Solve for \(b\):
\(b=1 - 2=-1\)

Step3: Write the equation

The slope - intercept form is \(y=mx + b\), with \(m = 1\) and \(b=-1\)
So the equation is \(y=x - 1\)

Answer:

\(y=x - 1\)