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 \((4, 9)\) and \((8, 3)\).

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

The formula for slope is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(4,9)\) and \((x_2,y_2)=(8,3)\). Then:

$$ m=\frac{3 - 9}{8 - 4}=\frac{-6}{4}=-\frac{3}{2} $$

Step3: Use point - slope form to find the equation

The point - slope form is \(y - y_1=m(x - x_1)\). Using the point \((4,9)\) and \(m =-\frac{3}{2}\):

$$ y - 9=-\frac{3}{2}(x - 4) $$

Expand the right - hand side:

$$ y - 9=-\frac{3}{2}x+6 $$

Add 9 to both sides:

$$ y=-\frac{3}{2}x + 6+9 $$

$$ y=-\frac{3}{2}x+15 $$

Answer:

\(y =-\frac{3}{2}x + 15\)