Question

question 7 (multiple choice worth 2 points)
(04.05 mc)
determine the equation for the line of best fit to represent the data.
$\bigcirc y = \frac{2}{3}x + 4$
$\bigcirc y = -\frac{2}{3}x + 4$
$\bigcirc y = -\frac{3}{2}x + 4$
$\bigcirc y = -\frac{2}{3}x - 4$

Explanation:

Step1: Determine the slope sign

The line of best fit is decreasing, so the slope \(m\) is negative.

Step2: Estimate the slope

Pick two points approximately on the line. Let's assume \((0,4)\) (y - intercept) and \((3,2)\).
The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substitute \(x_1 = 0,y_1=4,x_2 = 3,y_2 = 2\) into the formula:
\(m=\frac{2 - 4}{3-0}=\frac{- 2}{3}\)

Step3: Determine the y - intercept

The line crosses the y - axis at \(y = 4\), so \(b = 4\)

Step4: Write the equation of the line

The equation of a line is \(y=mx + b\). Substitute \(m=-\frac{2}{3}\) and \(b = 4\)
\(y=-\frac{2}{3}x + 4\)

Answer:

\(y =-\frac{2}{3}x+4\) (the second option)