Question 124433
I am guessing you have learned the point-slope form of a linear equation, y-y1=m(x-x1), where m is the slope and (x1,x2) is the point.  So, for your line, x1=5 and y1=-1.  That means we just need m.  We have the equation x-3y=6, but that does not immediately tell us the slope.  But do you remember the first form of a linear equation you learned? It was probably y=mx+b, where m is the slope.  This equation is very close to that, so let's just play with it until it looks exact, and then we'll see m, the slope.
First get the y term alone: -3y=6-x
Now divide by -3: y=-2+(1/3)x
Switch the terms so the x term is before the constant: y=(1/3)x-2
m=1/3
So we have a point and a slope- put it into the form at the beginning.
y+1=(1/3)(x-5)
This can also be written y+1=(x-5)/3