How do you write in point-slope form an equation of the line that passes through the point (1, 3) with slope -2?
Use the point-slope formula. The equation of a line of slope m
m
through (x0, y0)
(
x
0
,
y
0
)
is
y−y0=m(x−x0).
y
−
y
0
=
m
(
x
−
x
0
)
.
Let
(x0, y0)=(1, 3) and m=−2.
(
x
0
,
y
0
)
=
(
1
,
3
)
and
m
=
−
2
.
Then the equation of the required line is
y−3=−2(x−1).
y
−
3
=
−
2
(
x
−
1
)
.
Use the distributive rule and this is
y−3=−2x+2.
y
−
3
=
−
2
x
+
2
.
To get it In the slope-intercept form of
y=mx+b,
y
=
m
x
+
b
,
where b
b
is the second coordinate, that is, the ordinate of the y
y
intercept (0, b),
(
0
,
b
)
,
get y
y
by itself and
y=−2x+2+3.
y
=
−
2
x
+
2
+
3
.
Combine like terms and
y=−2x+5
y
=
−
2
x
+
5
and 5
5
is the ordinate of the y
y
intercept (0, 5).
(
0
,
5
)
.
In the standard form of
ax+by+c=0
a
x
+
b
y
+
c
=
0
it is
2x+y−5=0.
2
x
+
y
−
5
=
0
.
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