Answer:
A.
y
=
−
2
x
−
3
.
Explanation:
First, rewrite the equation in slope-intercept form:
y
=
m
x
+
b
.
−
x
+
2
y
=
4
⇒
2
y
=
x
+
4
⇒
y
=
1
2
x
+
2
So the slope of the given line is
m
=
1
2
.
Lines that are perpendicular have slopes that are negative reciprocals of each other. Meaning, if a line has slope
m
, then a line perpendicular to this has slope
m
*
=
−
1
m
. That means the slope of our perpendicular line is
m
*
=
−
1
1
/
2
=
−
2
.
Knowing the new slope and a point, we can find an equation for our perpendicular line by using the slope-point equation
y
−
y
1
=
m
(
x
−
x
1
)
, or by plugging in the given
(
x
,
y
)
point (and the new slope
m
*
) into
y
=
m
x
+
b
to find
b
for the new line.
y
−
y
1
=
m
(
x
−
x
1
)
⇒
y
−
1
=
−
2
[
x
−
(
−
2
)
]
⇒
y
−
1
=
−
2
[
x
+
2
]
⇒
y
=
−
2
x
−
3
or
y
=
m
x
+
b
⇒
1
=
−
2
(
−
2
)
+
b
⇒
1
=
4
+
b
⇒
b
=
−
3
∴
y
=
m
x
+
b
becomes
y
=
−
2
x
−
3
.
Step-by-step explanation:
