Step-by-step explanation:
the equation of a line in
slope-intercept form
is.
∙
x
y
=
m
x
+
b
where m is the slope and b the y-intercept
rearrange
2
x
−
3
y
=
12
into this form
subtract 2x from both sides
⇒
−
3
y
=
−
2
x
+
12
divide all terms by
−
3
⇒
y
=
2
3
x
−
4
←
in standard form
with
m
=
2
3
given a line with slope m then the slope of a line
perpendicular to it is
∙
x
m
perpendicular
=
−
1
m
⇒
m
perpendicular
=
−
1
2
3
=
−
3
2
⇒
y
=
−
3
2
x
+
b
←
is the partial equation
to find b substitute
(
2
,
6
)
into the partial equation
6
=
−
3
+
b
⇒
b
=
6
+
3
=
9
⇒
y
=
−
3
2
x
+
9
←
equation of perpendicular line