Answer:
it is 2
x
−
3
y
=
−
12
sorry if you dont get it bc the way i put it but here.........
Explanation:
The equation:
y
=
2
3
x
+
4
is in slope intercept form, which is a standard form of equation for a line.
Subtracting
y
from both sides, we get:
0
=
2
3
x
−
y
+
4
Subtracting
4
from both sides we get:
−
4
=
2
3
x
−
y
Multiplying both sides by
3
and transposing, we get:
2
x
−
3
y
=
−
12
This is in what some authors call standard form:
A
x
+
B
y
=
C
with a preference that
A
is a positive integer.
Note that:
The coefficients
A
,
B
and
C
are not unique. You can multiply them all by the same non-zero factor to get another equation for the same line.
If the line is horizontal, then
A
=
0
and cannot be a positive integer.
There may be additional "rules" to prefer
B
to be an integer too, but that would not be possible in the case of lines with irrational slope.
Some authors do not specify that
A
should be an integer.
Note that if you wanted the standard form of a polynomial, then the following form would be preferred:
A
x
+
B
y
+
C
=
0
In our example, that would be
2
x
−
3
y
+
12
=
0
In the context of equations of lines, this is sometimes known as general form.
For standard polynomial form, integer coefficients with positive
x
coefficient and no common factor are preferred if possible.