Write an equation of the line that passes through 9, 6 and is perpendicular to the line whose equation is y equals -1 over 3 x + 7

If the line that goes through (9, 6) is perpendicular to y = -1/3x + 7, then their slopes will be opposite reciprocals.  The slope of the line given is -1/3.  The opposite reciprocal of -1/3 is +3.  If we have our new line passing through point with x coordinate 9 and y coordinate 6, we will use that x and y and the slope of 3 to solve the slope-intercept equation for b.  Like this:  9 = 3(6) + b.  9 = 18 + b and b = -9.  That means that the new equation, the one that is perpendicular to the given line, is y = 3x - 9.