Answer:
The correct options are b and c.
Step-by-step explanation:
The given equation is
[tex]y=\frac{2}{3}x-4[/tex]
The slope intercept form of a linear equation is
[tex]y=mx+b[/tex]
In option a,
[tex]3x-2y=4[/tex]
[tex]3x-4=2y[/tex]
Divide both sides by 2.
[tex]\frac{3}{2}x-2=y[/tex]
Therefore option a is incorrect.
Similarly rewrite all equations in their slope intercept form.
In option b,
[tex]2x-3y=12[/tex]
[tex]2x-12=3y[/tex]
[tex]\frac{2}{3}x-4=y[/tex]
Therefore option b is correct.
In option c,
[tex]-4(2x-3y)=-4(12)[/tex]
[tex]2x-3y=12[/tex]
[tex]2x-12=3y[/tex]
[tex]\frac{2}{3}x-4=y[/tex]
Therefore option c is correct.
In option d,
[tex]2(x+6)=3y[/tex]
[tex]2x+12=3y[/tex]
[tex]\frac{2}{3}x+4=y[/tex]
Therefore option d is incorrect.
In option e,
[tex]2x-3y=4[/tex]
[tex]2x-4=3y[/tex]
[tex]\frac{2}{3}x-\frac{4}{3}=y[/tex]
Therefore option e is incorrect.
