Answer:
-2x+3y=11 and y= 2/3x-1
Explanation:
As a rule, parallel lines are defined as those that have the same gradient.
As such, the easiest way to solve this problem is to rearrange all possible answers into the form of y = mx + c, where c is a constant, and m is the gradient, and can be easily identified. Hence the original line would be:
-2x + 3y = 12
3y = 12 + 2x
y = 2/3x + 4
We can then continue this process of rearranging the equations through the use of algebra to come up with these answers for the other equations:
-2x + 3y = 11 → y = 2/3x + 11/3
-2x + y = 12 → y = 2x + 12
3x + 2y = -2 → y = - 3/2x - 1
y = 2/3x - 1 → y = 2/3x - 1
Now we can just look for the ones with the same gradient (the number before x) to our original equation (m = 2/3). Hence the lines parallel to -2x + 3y = 12 are:
-2x+3y=11 and y= 2/3x-1
Hope that helps!