What is the equation of the line of best fit?

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:

[tex]m\text{ = }\frac{Y2-Y1}{X2-X1}[/tex]

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:

[tex]m\text{ = }\frac{Y2-Y1}{X2-X1}=\text{ }\frac{1-2}{1-(-2)}=\text{ }\frac{-1}{1+2}=\frac{-1}{3}[/tex]

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

[tex]y\text{ = }\frac{-1}{3}x\text{ + b}[/tex]

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:

[tex]1\text{= }\frac{-1}{3}(0)\text{ + b}[/tex]

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

[tex]y\text{ = }\frac{-1}{3}x\text{ +}1[/tex]