Question

which equation of a line of best - fit reflects a negative correlation?
$y = \frac{1}{70}x + 312$
$y = \frac{-83}{-27}x + 15$
$y = 8x - 2$
$y = -6x + 13$

Explanation:

Step1: Recall the slope - correlation relationship

In the equation of a line \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept), a negative correlation is represented by a negative slope (\(m<0\)).

Step2: Analyze each equation's slope

• For \(y=\frac{1}{70}x + 312\), the slope \(m=\frac{1}{70}>0\).
• For \(y=\frac{- 83}{-27}x + 15=\frac{83}{27}x + 15\), the slope \(m = \frac{83}{27}>0\).
• For \(y = 8x-2\), the slope \(m = 8>0\).
• For \(y=-6x + 13\), the slope \(m=-6<0\).

Answer:

\(y=-6x + 13\)