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

The two yellow points are \((4, 6)\) and \((8, 0)\).

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

The formula for slope is \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
Substituting the points \((4, 6)\) (where \(x_1 = 4\), \(y_1 = 6\)) and \((8, 0)\) (where \(x_2 = 8\), \(y_2 = 0\)):
\( m = \frac{0 - 6}{8 - 4} = \frac{-6}{4} = -\frac{3}{2} \)

Step3: Find the y-intercept (\(b\))

Using the slope-intercept form \( y = mx + b \) and one of the points, say \((8, 0)\):
Substitute \(x = 8\), \(y = 0\), and \(m = -\frac{3}{2}\) into the equation:
\( 0 = -\frac{3}{2}(8) + b \)
\( 0 = -12 + b \)
Solving for \(b\), we get \( b = 12 \)

Step4: Write the equation

Substitute \(m = -\frac{3}{2}\) and \(b = 12\) into the slope-intercept form \( y = mx + b \):
\( y = -\frac{3}{2}x + 12 \)

Answer:

\( y = -\frac{3}{2}x + 12 \)