Answer: C
Step-by-step explanation:
General form is in Ax+By+C. To do this, you move everything onto one side.
[tex]\frac{3}{2}x -y+3=0[/tex]
This should be the general form, but this is not correct in these answer choices! Let's try this another way to get Ax+By+C by making Ax not a fraction.
[tex]y=\frac{3}{2} x-3[/tex]
[tex]y+3=\frac{3}{2} x[/tex]
[tex]2(y+3)=3x[/tex]
[tex]2y+6=3x[/tex]
[tex]3x-2y-6=0[/tex]
This may seem incorrect, but we can always check our answer by plugging in numbers.
In our slope intercept form, let's say x=2. What would be our y?
[tex]y=\frac{3}{2} (2)-3[/tex]
[tex]y=3-3[/tex]
[tex]y=0[/tex]
Now we know our coordinates should be (2, 0). When we rewrite the slope-intercept form, we should still get 0 when we plug in x=2 and y=0. Let's check on all answer choices to see which one works.
A. Correct
-3(2)+2(0)+6
-6-6=0
0=0
B. Incorrect
3/2(2)-(0)+3
3+3=6
6≠0
C. Correct
3(2)-2(0)-6
6-6=0
0=0
D. Incorrect; not general form
2(0)=3(2)-6
0=6-6
Now, you can see that A and C are both correct, but the main difference, is that you want to make A positive. The only option where A is positive is in answer C.
