Answer:
The perpendicular line would be y = -3/2x - 1
Step-by-step explanation:
First we have to solve the first equation for y.
2x - 3y = 9
-3y = -2x + 9
y = 2/3x - 3
In order to find the equation of this line, we first have to note that perpendicular lines have opposite and reciprocal slopes. Therefore, since the original line has a slope of 2/3, we know the new line will have a slope of -3/2. Now we can use that information along with the given point in point-slope form to find the equation.
y - y1 = m(x - x1)
y + 4 = -3/2(x - 2)
y + 4 = -3/2x + 3
y = -3/2x - 1
