She did it using the point-slope form.  I'll do it using
only the slope-intercept form y = mx+b


y = 2x+5

compare that to

y = mx+b

And see that the slope is m=2 and the y-coordinate of the y-intercept
is b=5, and so the y-intercept is (0,5), but you only need the slope

The slope of any line parallel to it will also have slope m=2 but
will have a different value for b.  So substitute b=2 in

 y = mx+b

and get

 y = 2x+b

Then since it goes through the point (2,1) we substitute x=2 and y=1

 1 = 2(2)+b

 1 = 4+b
-3 = b

Now substitute -3 for b in

 y = 2x+b

and get:

 y = 2x-3

Edwin