Find an equation in standard form and slope intercept form: has x-intercept 3 and y-intercept 6

2
x
+
3
y
=
6

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

What’s the improper fraction?