Answer :
Answer:
A line is parallel to y=4x+5 and passes through the point (-1,6). Find the equation of the line L in the form y=ax+b. Find also the coordinates of its intersections with the axes.
To solve the problem, let's break it down into two parts:
1. Equation of the Line
L
L
The given line is
y
=
4
x
+
5
y=4x+5. The slope
m
m of this line is 4, since the equation is in the form
y
=
m
x
+
c
y=mx+c.
For two lines to be parallel, they must have the same slope. Therefore, the line
L
L must also have a slope of 4. The equation of line
L
L can be written as:
y
=
4
x
+
b
y=4x+b
Now, we need to find the value of
b
b using the point
(
−
1
,
6
)
(−1,6), which the line
L
L passes through.
Substitute
x
=
−
1
x=−1 and
y
=
6
y=6 into the equation:
6
=
4
(
−
1
)
+
b
6=4(−1)+b
6
=
−
4
+
b
6=−4+b
b
=
10
b=10
So, the equation of the line
L
L is:
y
=
4
x
+
10
y=4x+10
2. Intersections with the Axes
Intersection with the
y
y-axis:
To find the intersection with the
y
y-axis, set
x
=
0
x=0:
y
=
4
(
0
)
+
10
=
10
y=4(0)+10=10
So, the intersection with the
y
y-axis is
(
0
,
10
)
(0,10).
Intersection with the
x
x-axis:
To find the intersection with the
x
x-axis, set
y
=
0
y=0:
0
=
4
x
+
10
0=4x+10
4
x
=
−
10
4x=−10
x
=
−
5
2
x=−
2
5
So, the intersection with the
x
x-axis is
(
−
5
2
,
0
)
(−
2
5
,0).
Final Answer:
Equation of the line
L
L:
y
=
4
x
+
10
y=4x+10
Intersection with the
y
y-axis:
(
0
,
10
)
(0,10)
Intersection with the
x
x-axis:
(
−
5
2
,
0
)
(−
2
5
,0)
