Given
(2, 9)
(13, 20)
Procedure
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
First, let's find what m is, the slope of the line...
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ m=\frac{20-9}{13-2} \\ m=\frac{11}{11} \\ m=1 \end{gathered}[/tex]Now, what about b, the y-intercept?
[tex]\begin{gathered} b=y-mx \\ b=20-1(13) \\ b=20-13 \\ b=7 \end{gathered}[/tex]The equation of the line that passes through the points
(2,9) and (13,20)
[tex]y=x+7[/tex]