Answer:The equation of perpendicular line is
y
=
−
5
3
x
+
17
3
.
Explanation:
The slope of the line
y
=
3
5
x
−
6
is
m
1
=
3
5
[obtained by
comparing standard slope-intercept form of line with slope
m
;
y
=
m
x
+
c
] . We know the product of slopes of two
perpendicular lines is
−
1
, i.e
m
1
⋅
m
2
=
−
1
or
3
5
⋅
m
2
=
−
1
or
m
2
=
−
5
3
. Let the equation of perpendicular line in
slope - intercept form is
y
=
m
x
+
c
;
m
=
m
2
=
−
5
3
∴
y
=
−
5
3
x
+
c
. The line passes through point
(
1
,
4
)
, which
will satisfy the equation of line
∴
4
=
−
5
3
⋅
1
+
c
∴
c
=
4
+
5
3
or
c
=
17
3
Hence the equation of perpendicular line is
y
=
−
5
3
x
+
17
3
