First, we must realize the slopes of perpendicular lines are negative reciprocals.
Second, the equation of a line is in the form of y=mx+b where m is the slope and b is the y-intercept.
Therefore, in the original equation, y=(1/3)x + 6, m (the slope) is 1/3. Because the negative reciprocal of this is the slope of the perpendicular line, m = -3/1 or -3.
Now we have y = -3x + b and must find b. Use the point given, (9,1), to solve for b.
y = -3x + b original equation
1 = -3(9) + b replacing (x,y) with (9,1)
1 = -27 + b multiply
1 + 27 = b add 27 to both sides
28 = b solve for b
Now we know m & b for the perpendicular line. Just need to put those numbers in the equation of a line and we're done:
y = mx + b equation of a line
y = -3x + 28 answer!