Question

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Answer 1

We know that the standard form is
ax + by = c
So, let's solve this problem to get correct answer
y = -2/3x + 4 { multiplying each term by 3 }
3y = -2x + 12  { according to the standard form equation our x variable should be on other side so let move that} { adding 2x on both sides }
2x + 3y =  12 
 Hence the correct option is B.

If you want to check your answer resolve your answer and see if you get the same quotient.
2x + 3y = 12
3y = -2x + 12 { subtracting both sides by -2x }
y = -2/3x + 12/3 {dividing both sides by 3 } 
y = -2/3x + 4 { same as the quotient }

Hence proved.

Answer 2

Standard form is ax+by=c so
y=-2/3x+4
add 2/3x to both sides
2/3x+y=4
make whole numbers for niceness
multipily by 3 to clear fraction
2x+3y=12

answer is second one