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.
