Question

frank created a scatter plot and drew a line of best fit, as shown.
what is the equation of the line of best fit that frank drew?
a. $y=-3x + 12$
b. $y=-3x + 16$
c. $y=-\frac{1}{3}x + 12$
d. $y=-\frac{1}{3}x + 16$

Explanation:

Step1: Find the y - intercept

The y - intercept is the value of y when x = 0. Looking at the line of best fit, when x = 0, y = 16. So the equation of the line is in the form \(y=mx + 16\).

Step2: Calculate the slope

Take two points on the line (for simplicity, assume the line passes through (0,16) and (6,14)).
The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Here, \(x_1 = 0,y_1 = 16,x_2=6,y_2 = 14\).
\(m=\frac{14 - 16}{6-0}=\frac{-2}{6}=-\frac{1}{3}\)

Answer:

D. \(y =-\frac{1}{3}x + 16\)