Respuesta :
Answer:
y = 3x
Step-by-step explanation:
Choose a point that the perpendicular line will pass through.
(
0
,
0
)
Combine
1
3
and
x
.
y
=
x
3
+
6
Use the slope-intercept form to find the slope.
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The slope-intercept form is
y
=
m
x
+
b
, where
m
is the slope and
b
is the y-intercept.
y
=
m
x
+
b
Using the slope-intercept form, the slope is
1
3
.
m
=
1
3
The equation of a perpendicular line to
y
=
x
3
+
6
must have a slope that is the negative reciprocal of the original slope.
m
perpendicular
=
−
1
1
3
Simplify
−
1
1
3
to find the slope of the perpendicular line.
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Multiply the numerator by the reciprocal of the denominator.
m
perpendicular
=
−
(
1
⋅
3
)
Multiply
3
by
1
.
m
perpendicular
=
−
1
⋅
3
Multiply
−
1
by
3
.
m
perpendicular
=
−
3
Find the equation of the perpendicular line using the point-slope formula.
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Using the point-slope form
y
−
y
1
=
m
(
x
−
x
1
)
, plug in
m
=
−
3
,
x
1
=
0
, and
y
1
=
0
.
y
+
0
=
−
3
(
x
+
0
)
Solve for
y
.
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Add
y
and
0
.
y
=
−
3
(
x
+
0
)
Add
x
and
0
.
y
=
−
3
x
Hello!
y=-1/3x+6
Perpendicular lines have slopes that are opposite reciprocals.
This means that if we have a slope of -1/3, its opposite reciprocal would be 3
Use Point-Slope form:
y-y1=m(x-x1)
y-4=3(x-2)
y-4=3x-6
y=3x-6+4
y=3x-2
Hope this helps you!
~Just a joyful teen
[tex]GraceRosalia[/tex]
