Respuesta :
To find the equation of the straight line passing through the point of intersection of the lines
3
x
−
y
−
6
=
0
3x−y−6=0 and
x
−
y
−
2
=
0
x−y−2=0 and the point (-1, 3), follow these steps:
Find the point of intersection of the given lines:
Solve the system of equations:
3
x
−
y
−
6
=
0
(Equation 1)
x
−
y
−
2
=
0
(Equation 2)
3x−y−6
x−y−2
=0(Equation 1)
=0(Equation 2)
Solve the system to find the values of
x
x and
y
y.
Once you have the point of intersection, use it along with the given point (-1, 3) to find the slope (
m
m) of the line.
m
=
y
2
−
y
1
x
2
−
x
1
m=
x
2
−x
1
y
2
−y
1
where
(
x
1
,
y
1
)
(x
1
,y
1
) is the point of intersection and
(
x
2
,
y
2
)
(x
2
,y
2
) is the given point.
With the slope and one of the points, use the point-slope form of a linear equation to find the equation of the line:
y
−
y
1
=
m
(
x
−
x
1
)
y−y
1
=m(x−x
1
)
Substitute the values of
m
m,
x
1
x
1
, and
y
1
y
1
to get the final equation.
Let's go through the steps:
Solve the system of equations:
3
x
−
y
−
6
=
0
(Equation 1)
x
−
y
−
2
=
0
(Equation 2)
3x−y−6
x−y−2
=0(Equation 1)
=0(Equation 2)
Solving this system will give you the point of intersection.
Once you have the point of intersection, use it along with the given point (-1, 3) to find the slope (
m
m):
m
=
y
2
−
y
1
x
2
−
x
1
m=
x
2
−x
1
y
2
−y
1
Use the point-slope form to find the equation of the line:
y
−
y
1
=
m
(
x
−
x
1
)
y−y
1
=m(x−x
1
)
Substitute the values of
m
m,
x
1
x
1
, and
y
1
y
1
to get the final equation.
3
x
−
y
−
6
=
0
3x−y−6=0 and
x
−
y
−
2
=
0
x−y−2=0 and the point (-1, 3), follow these steps:
Find the point of intersection of the given lines:
Solve the system of equations:
3
x
−
y
−
6
=
0
(Equation 1)
x
−
y
−
2
=
0
(Equation 2)
3x−y−6
x−y−2
=0(Equation 1)
=0(Equation 2)
Solve the system to find the values of
x
x and
y
y.
Once you have the point of intersection, use it along with the given point (-1, 3) to find the slope (
m
m) of the line.
m
=
y
2
−
y
1
x
2
−
x
1
m=
x
2
−x
1
y
2
−y
1
where
(
x
1
,
y
1
)
(x
1
,y
1
) is the point of intersection and
(
x
2
,
y
2
)
(x
2
,y
2
) is the given point.
With the slope and one of the points, use the point-slope form of a linear equation to find the equation of the line:
y
−
y
1
=
m
(
x
−
x
1
)
y−y
1
=m(x−x
1
)
Substitute the values of
m
m,
x
1
x
1
, and
y
1
y
1
to get the final equation.
Let's go through the steps:
Solve the system of equations:
3
x
−
y
−
6
=
0
(Equation 1)
x
−
y
−
2
=
0
(Equation 2)
3x−y−6
x−y−2
=0(Equation 1)
=0(Equation 2)
Solving this system will give you the point of intersection.
Once you have the point of intersection, use it along with the given point (-1, 3) to find the slope (
m
m):
m
=
y
2
−
y
1
x
2
−
x
1
m=
x
2
−x
1
y
2
−y
1
Use the point-slope form to find the equation of the line:
y
−
y
1
=
m
(
x
−
x
1
)
y−y
1
=m(x−x
1
)
Substitute the values of
m
m,
x
1
x
1
, and
y
1
y
1
to get the final equation.
