Answer: y+2x−1=0
Step-by-step explanation: Let's say A is the point (−1,3) and B is the point (3,−5)
The equation of a line that passes through two points is
y−y0=m(x−x0)
Replace x,x0,y and y0
by the coordinates of the two points to find your slope
⇒m
.
It doesn't matter which point you choose to replace
x,x0,y and y0 with as long as you pair xwith yand x0 with
y
0
.
m
=
y
−
y
0
x
−
x
0
=
−
5
−
3
3
−
(
−
1
)
=
−
5
−
3
3
+
1
=
−
2
Now, all you have to do is to choose either the coordinates of
A
or
B
to replace in the equation of a line that passes through two points
⇒
y
−
y
0
=
m
(
x
−
x
0
)
. You are only going to replace
x
0
and
y
0
.
I'm using the point
A
(
−
1
,
3
)
⇒
y
−
y
0
=
m
(
x
−
x
0
)
⇒
y
−
3
=
−
2
(
x
+
1
)
⇒
y
−
3
=
−
2
x
−
2
⇒
y
+
2
x
−
1
=
0
is your line.Let's say
A
is the point
(
−
1
,
3
)
and
B
is the point
(
3
,
−
5
)
The equation of a line that passes through two points is
y
−
y
0
=
m
(
x
−
x
0
)
Replace
x
,
x
0
,
y
and
y
0
by the coordinates of the two points to find your slope
⇒
m
.
It doesn't matter which point you choose to replace
x
,
x
0
,
y
and
y
0
with as long as you pair
x
with
y
and
x
0
with
y
0
.
m
=
y
−
y
0
x
−
x
0
=
−
5
−
3
3
−
(
−
1
)
=
−
5
−
3
3
+
1
=
−
2
Now, all you have to do is to choose either the coordinates of
A
or
B
to replace in the equation of a line that passes through two points
⇒
y
−
y
0
=
m
(
x
−
x
0
)
. You are only going to replace
x
0
and
y
0
.
I'm using the point
A
(
−
1
,
3
)
⇒
y
−
y
0
=
m
(
x
−
x
0
)
⇒
y
−
3
=
−
2
(
x
+
1
)
⇒
y
−
3
=
−
2
x
−
2
⇒
y
+
2
x
−
1
=
0
is your line.