Find the eqation of the line perpendicular to y=3x-6 that runs through the point (-1, -3)

The coefficient of x in the equation of the given line, 3, is its slope. The slope of the perpendicular line is the negatve reciprocal of that, -1/3. You now have the slope and a point on the perpendicular line, so you can write its equation using the point-slope form:
  y = m(x -x₁) +y₁
where m is the slope and (x₁, y₁) is the point.

An equation for your perpendicular line is
  y = (-1/3)(x -(-1)) -3
  y = (-1/3)x -10/3

The slope-intercept form of the equation of the perpendicular line is ...
  y = (-1/3)x -10/3

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