Question

manny created a scatter plot and drew a line of best fit, as shown. what is the equation of the line of best fit that manny drew? a. $y = 2x + 7$ b. $y = 2x + 9$ c. $y = \frac{1}{2}x + 7$ d. $y = \frac{1}{2}x + 9$

Explanation:

Step1: Find the y - intercept

The y - intercept \(b\) is the value of \(y\) when \(x = 0\). Looking at the line, when \(x=0\), \(y = 7\). So \(b = 7\).

Step2: Calculate the slope

The slope \(m\) of a line is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points on the line. When \(x = 1\), \(y\approx9\) (from the line), and when \(x = 2\), \(y\approx11\). Then \(m=\frac{11 - 9}{2 - 1}=\frac{2}{1}=2\).
The equation of a line is \(y=mx + b\). Substituting \(m = 2\) and \(b = 7\) into the equation, we get \(y = 2x+7\).

Answer:

A. \(y = 2x + 7\)