Answer:
[tex]\textsf{a)}\quad y=-\dfrac{2}{3}x+4[/tex]
Step-by-step explanation:
A line of best fit is a straight line that represents the general trend in a set of data points. The line is determined by minimizing the overall distance between the line and the data points.
If we add a line of best fit to the given scatter plot (see attachment):
- The line crosses the y-axis at (0, 4).
- The line crosses the x-axis at (6, 0).
We can use these two points to calculate the slope of the line by substituting them into the slope formula:
[tex]\textsf{Slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-4}{6-0}=-\dfrac{4}{6}=-\dfrac{2}{3}[/tex]
The line intercepts the y-axis at y = 4, so the y-intercept is 4.
Substitute the found slope and the y-intercept into the slope-intercept formula to create the equation of the line of best fit:
[tex]\begin{aligned}y&=mx+b\\\implies y&=-\dfrac{2}{3}x+4\end{aligned}[/tex]
Therefore, the equation of the line of best fit is
[tex]\boxed{y=-\dfrac{2}{3}x+4}[/tex]
