Explanation:
Slope-intercept form is given by
y
=
m
x
+
b
, where
m
is the slope of the line and
b
is the
y
-intercept of the line, or the value of
y
where the line crosses the
y
-axis.
Given that the slope of the line is
2
, we have
m
=
2
, and because the line crosses the
y
-axis at the point
(
0
,
0
)
, where
y
=
0
and
x
−
0
, we have:
y
=
2
x
+
0
Or, equivalently,
y
=
2
x
If the point given were not the origin, you could use
y
=
m
x
+
b
to find
b
by plugging the
x
and
y
value of the point in for
x
and
y
in the equation along with the given slope
m
and solving for
b
.
Given
m
=
2
and
(
x
,
y
)
=
(
0
,
0
)
:
0
=
2
(
0
)
+
b
⇒
0
=
b
We would then put this value back into
y
=
m
x
+
b
for
b
, along with the slope
m
, yielding the same answer as above:
y
=
2
x
.
