Question

What is the equation of the line of best fit?

Answer 1

Question:

What is the equation of the line of best fit?​

Solution:

By definition, the equation of the line is given by:

y = mx+b

where m is the slope of the line and b is the y-coordinate of the y-intercept. Now, by definition the slope of the line is given by the following equation:

$m\text{ = }\frac{Y2-Y1}{X2-X1}$

where (X1,Y1) and (X2,Y2) are points on the line (in our case points on the table). Taking into account this, take any two points on the table, for example

(X1,Y1) = (-2,2)

(X2,Y2) = (1,1)

Put these points in the equation for the slope:

$m\text{ = }\frac{Y2-Y1}{X2-X1}=\text{ }\frac{1-2}{1-(-2)}=\text{ }\frac{-1}{1+2}=\frac{-1}{3}$

then, the slope of the line is -1/3. Put this value on the equation of the line we get:

$y\text{ = }\frac{-1}{3}x\text{ + b}$

now, we want to find b. For this, take any two points in the table, and put these points in the previous equation. Take for example (x,y) =(0,1), then we have:

$1\text{= }\frac{-1}{3}(0)\text{ + b}$

then, we can conclude that b = 1. Thus, we can conclude that the equation of the line is:

$y\text{ = }\frac{-1}{3}x\text{ +}1$