When asked to write a point slope equation for the line shown, a student wrote y-6=3(x-3). how can she fix this to write the correct equation?

The form of the point slope equation for the line is

y -y1 = m (x -x1)

Where m is the slope and (x1,y1) is the point considered (belongin to the line)

You didn't include any graph or drawing of the line.

The procedure is to calculate the slope which is the change of y over the change of and substitue m.

Then pick one of the points that belong to the line with wich you wll have 

m, x1 and y1 and can write the correct equation.

Using the rise/run rule. you would get 2/6.simp. 1/3