ok, so the equation of a line that passe through the point (x1,y1) and has a slope of m is
y-y1=m(x-x1)
given slope (or gradient) of 2 and point (1,4)
y-4=2(x-1)
you can get several forms
point slope: y-y1=m(x-x1)
slope intercept: y=mx+b
standard form: ax+by=c
so, sloving for each
y-4=2(x-1)
y-4=2x-2
y=2x+2, that's slope intercept
2x-y=-2, tat's standard form