To write an equation parallel to another equation through a given ordered pair, you can follow these steps:
Determine the Slope:
The two parallel lines will have the same slope. If the given equation is in the form
�
=
�
�
+
�
y=mx+b, where
�
m is the slope, then the parallel line should also have a slope of
�
m.
Use the Ordered Pair:
Substitute the coordinates of the given point (ordered pair) into the equation.
This will give you the
�
y-intercept (
�
b).
Write the Equation:
Write the equation in the form
�
=
�
�
+
�
y=mx+b using the determined slope and
�
y-intercept.
For example, let's say you have the line
�
=
2
�
+
3
y=2x+3 and you want to find a parallel line through the point
(
1
,
4
)
(1,4):
Determine the Slope:
The slope of the given line is
2
2.
Use the Ordered Pair:
Substitute
�
=
1
x=1 and
�
=
4
y=4 into the equation:
4
=
2
(
1
)
+
�
4=2(1)+b.
Solve for
�
b:
�
=
2
b=2.
Write the Equation:
The equation of the parallel line is
�
=
2
�
+
2
y=2x+2.
So, the parallel line to
�
=
2
�
+
3
y=2x+3 that passes through the point
(
1
,
4
)
(1,4) is
�
=
2
�
+
2
y=2x+2.