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 the slope \( m \)

The formula for slope is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let the two yellow points be \((x_1,y_1)=(4,7)\) and \((x_2,y_2)=(8,3)\).

$$ m=\frac{3 - 7}{8 - 4}=\frac{-4}{4}=- 1 $$

Step2: Use the slope - intercept form \( y = mx + b \) to find \( b \)

Substitute \( m=-1\), \(x = 4\), and \(y = 7\) into \(y=mx + b\).

$$ 7=-1\times4 + b $$

$$ 7=-4 + b $$

$$ b=7 + 4=11 $$

Step3: Write the equation

Substitute \(m=-1\) and \(b = 11\) into \(y=mx + b\).

$$ y=-x + 11 $$

Answer:

\(y=-x + 11\)