Question 457603
Which of the following is the equation of a line perpendicular to
9y = 3x + 5 that passes through (-2,3)?
y = -3x - 3
3y - 6x = 10
y - 3x = -3
y = -3x - 6 
.
Begin by finding the slope of:
9y = 3x + 5
y = (3/9)x + 5/9
y = (1/3)x + 5/9 (slope-intercept form)
we see that the slope is 1/3
a line perpendicular would have to have a slope that is the negative reciprocal -- which is -3
easiest way to inspect the four given answer looking for a -3 slope
y = -3x - 3  (yes)
3y - 6x = 10  (no)
y - 3x = -3  (no)
y = -3x - 6  (yes)
.
now, you only have to pick from two:
y = -3x - 3
y = -3x - 6 
to eliminate one we use the given point:(-2,3)
Only the "top" equation works:
y = -3x - 3
3 = -3(-2) - 3
3 = 6 - 3
3 = 3
.
Answer: y = -3x - 3