Answer:
actually : none of them do. your teacher made a mistake (of you mistyped her something).
I suspect somebody mistyped C (see below), and that should have been the correct answer.
Explanation:
the slope in a
y = ... form
is always the factor of x.
therefore, the slope of
y / (-2/3)x + 5
is
-2/3
a perpendicular slope turns the original slope ratio upside down and flips the sign.
in our case :
3/2
to check and compare we need to transform all the answer options into y = ... forms :
A.
2x - 3y = 6
-3y = -2x + 6
3y = 2x - 6
y = (2/3)x - 2
no, 2/3 is NOT the needed 3/2.
B.
2x + 3y = 6
3y = -2x + 6
y = (-2/3)x + 2
no, -2/3 is NOT the needed 3/2
C.
2x - 3y = 6
this is the same as A.
I assume it was meant to be 3x - 2y = 6.
then this would have been the correct answer.
but as it is written : no, like A.
D.
3x + 2y = 6
2y = -3x + 6
y = (-3/2)x + 3
no, -3/2 is NOT the needed 3/2