2
x
+
3
y
=
6
Step-by-step explanation:
the equation of a line in
standard form
is.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
∣
∣
∣
2
2
A
x
+
B
y
=
C
2
2
∣
∣
∣
−−−−−−−−−−−−−−−−−
where A is a positive integer and B, C are integers
the equation of a line in
slope-intercept form
is.
∙
x
y
=
m
x
+
b
where m is the slope and b the y-intercept
to calculate m use the
gradient formula
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
∣
∣
∣
2
2
m
=
y
2
−
y
1
x
2
−
x
1
2
2
∣
∣
∣
−−−−−−−−−−−−−−−−−
let
(
x
1
,
y
1
)
=
(
3
,
0
)
and
(
x
2
,
y
2
)
=
(
0
,
2
)
⇒
m
=
2
−
0
0
−
3
=
−
2
3
⇒
y
=
−
2
3
x
+
2
←
in slope-intercept form
multiply through by 3
⇒
3
y
=
−
2
x
+
6
⇒
2
x
+
3
y
=
6
←
in standard form