Perpendicular lines have slopes that are the inverse reciprocal of each other. For example, if you have a line with slope 2, its perpendicular line will have slope -1/2.
You can solve this problem by doing the following:
(1) Put the equation for the line (6x-y=7) in standard form (y=mx + b).
(2) Determine the slope of the perpendicular line: m2 = -1/m.
(3) Find the y-intercept: y2 = m2x + b2, substituting your point gives -1 = m2(-6) + b2. Solve for b2.
(4) The equation of the perpendicular line is y = m2x + b2, using the values for m2 and b2 you calculated above.