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: Identify the two yellow points

From the scatter plot, the two yellow points are \((5, 6)\) and \((7, 4)\).

Step2: Calculate the slope (\(m\))

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting \(x_1 = 5\), \(y_1 = 6\), \(x_2 = 7\), \(y_2 = 4\) into the formula:
\(m=\frac{4 - 6}{7 - 5}=\frac{-2}{2}=-1\)

Step3: Use point - slope form to find the equation

The point - slope form of a line is \(y - y_1=m(x - x_1)\). Let's use the point \((5, 6)\) and \(m=-1\).
Substitute into the formula: \(y - 6=-1(x - 5)\)
Simplify the equation:
\(y - 6=-x + 5\)
Add 6 to both sides: \(y=-x+5 + 6\)
\(y=-x + 11\)

Answer:

\(y=-x + 11\)