What is the equation of a line that is perpendicular to −x+3y=9 and passes through the point (−3, 2) ?

• rearrange into form y = mx + c:
3y = 9 + x
y = 9/3 + x/3
y = 1/3x + 3

• substitute the gradient, 1/3, into the formula "m1 X m2 = -1" to find m2, which is the perpendicular of the gradient:
1/3 X m2 = -1
m2 = -3

• substitute x and y values of (-3, 2) into new equation, y = -3x + c, and rearrange, to find c and complete the equation:
2 = -3(-3) + c
2 = 9 + c
2 - 9 = c
c = -7

y = -3x - 7 is perpendicular to the line and passes through the point (-3, 2)