Answer:
Step-by-step explanation:Parallel Lines have the SAME SLOPE
We first Find the Slope of the line
y
=
2
x
+
3
The Slope Intercept Form of the equation of a given line is:
y
=
m
x
+
c
where
m
is the Slope of that line, and
c
is the Y intercept.
For this line, the Slope is
2
So the Slope of the line PARALLEL to
y
=
2
x
+
3
will also be
2
. And we are given that it passes through the point
(
−
3
,
4
)
With this, we can use the Point Slope form to find the equation of the line.
The Point-Slope form of the Equation of a Straight Line is:
(
y
−
k
)
=
m
⋅
(
x
−
h
)
m
is the Slope of the Line
(
h
,
k
)
are the co-ordinates of any point on that Line.
Here, we have been given the coordinates
(
h
,
k
)
of 1 point on that line as
(
−
3
,
4
)
And the Slope
m
is
2
Substituting the values of
h
,
k
and
m
in the Point-Slope form, we get
(
y
−
4
)
=
(
2
)
⋅
(
x
−
(
−
3
)
)
The above will be the Equation of the Line in Point-Slope form.
If we need it in the Slope Intercept Form, we need to follow these steps:
Modifying the equation, we get:
(
y
−
4
)
=
2
⋅
(
x
+
3
)
y
−
4
=
2
x
+
6
y
=
2
x
+
6
+
4
We get the equation of the line as :
y
=
2
x
+
10
The graph will look like this:
graph{y=2x+10 [-10, 10, -5, 5]}