Question

what is the equation of the trend line in the scatter plot?
use the two orange 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 orange points

The two orange points are \((5,3)\) and \((9,5)\).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substitute \((x_1,y_1)=(5,3)\) and \((x_2,y_2)=(9,5)\) into the formula:
\(m=\frac{5 - 3}{9 - 5}=\frac{2}{4}=\frac{1}{2}\).

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

Use the point \((5,3)\) and \(m = \frac{1}{2}\).
\(y-3=\frac{1}{2}(x - 5)\).

Step4: Convert to slope - intercept form \(y=mx + b\)

Expand the point - slope equation:
\(y-3=\frac{1}{2}x-\frac{5}{2}\).
Add 3 to both sides:
\(y=\frac{1}{2}x-\frac{5}{2}+3\).
Since \(3=\frac{6}{2}\), then \(y=\frac{1}{2}x+\frac{1}{2}\).

Answer:

\(y=\frac{1}{2}x+\frac{1}{2}\)