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 two points on the trend line

The two yellow points are \((30,30)\) and \((70,80)\).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substitute \(x_1 = 30,y_1 = 30,x_2 = 70,y_2 = 80\) into the formula:
\(m=\frac{80 - 30}{70 - 30}=\frac{50}{40}=\frac{5}{4}\)

Step3: Use the point - slope form \(y - y_1=m(x - x_1)\) to find the equation

Use the point \((30,30)\) and \(m = \frac{5}{4}\).
\(y-30=\frac{5}{4}(x - 30)\)
Expand: \(y-30=\frac{5}{4}x-\frac{150}{4}\)
\(y-30=\frac{5}{4}x - 37.5\)
Add 30 to both sides: \(y=\frac{5}{4}x- 7.5\)

Answer:

\(y=\frac{5}{4}x - 7.5\)