Data can be modeled by a linear equation if all of the points lay on the same line. This happens if every pair of points have the same slope, which we can calculate as
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
For example, the first two points have a slope of
[tex]m=\dfrac{5-(-3)}{4-2}=\dfrac{8}{2}=4[/tex]
The first and third point have a slope of
[tex]m=\dfrac{13-(-3)}{6-2}=\dfrac{16}{4}=4[/tex]
You can check that all the other pairs always share a slope of 4. This is enough to claim that the points lay on the same line.
To write the equation of the said line, we can use the following formula: given a point [tex](x_0,y_0)[/tex] and a slope [tex]m[/tex], the line passing through that point with that slope has equation
[tex]y-y_0=m(x-x_0)[/tex]
Plugging the coordinates of the first point (for example) and the slope we found out, we have
[tex]y-(-3)=4(x-2) \iff y +3= 4x-8 \iff y=4x-11[/tex]
