Answer:
y = (-3/2)x - 4
Step-by-step explanation:
Recall that a line perpendicular to a given line has a slope which is the negative reciprocal of the given line. The given line can be re-written as -3y = -2x + 13, or
y = (2/3)x - 13/3
and so the slope of a line perpendicular to this given line is -3/2.
Then the desired equation, in point-slope form, is
y - 5 = (-3/2)(x + 6) (This is in point-slope form.)
Alternatively,
2y - 10 = -3(x + 6) = -3x - 18, or
2y = 10 - 3x - 18, or
2y = -3x - 8, or y = (-3/2)x - 4 (This is in slope-intercept form.)
