The y-intercept is the value when x=0. The x-intercept of 3 corresponds to y=0, and the point on the line is (3,0). The y-intercept of 4 corresponds to x=0, and the point on the line is (0,4). ... Now that we have the slope, we can write the equation for the line in point-slope form. One quick way to do this is to use the fact that
3
⋅
4
=
12
to say an equation for this line is
4
x
+
3
y
=
12
(since, when
y
=
0
, it follows that
x
=
3
and when
x
=
0
it follows that
y
=
4
).
You could also find the slope of the line containing the points
(
x
,
y
)
=
(
3
,
0
)
and
(
x
,
y
)
=
(
0
,
4
)
as
Δ
y
Δ
x
=
4
−
0
0
−
3
=
−
4
3
so that the equation has the form
y
=
−
4
3
x
+
b
, where
b
is the
y
-intercept so the equation becomes
y
=
−
4
3
x
+
4
. This is equivalent to the last answer because you can multiply everything by 3 and rearrange to get
4
x
+
3
y
=
12.