When you write a line in the [tex] y=mx+q[/tex], [tex] m [/tex] is the slope of the line, and [tex] q [/tex] is the y-intercept, i.e. the y coordinate of the point [tex] (0,y) [/tex] belonging to the line.
The line passes through the point [tex] (0,2) [/tex], so [tex] q=2 [/tex]. As for the slope, we consider two points belonging to the line, and compute the following ratio:
[tex] m = \dfrac{\Delta y}{\Delta x} = \dfrac{y_2-y_1}{x_2-x_1} [/tex]
The two highlighted points are [tex] (1,3) [/tex] and [tex](4,6) [/tex]
So, the slope is
[tex] m = \dfrac{\Delta y}{\Delta x} = \dfrac{y_2-y_1}{x_2-x_1} = \dfrac{6-3}{4-1} = 1 [/tex]
The equation is thus [tex] y=x+2 [/tex]
