Question

Please help me with this.

Answer 1

1. x - 2y = -6

2. x + 3y = 0

Explanation:

The Standard form of an eqaution of a line:

`Ax+By=C`

1.

`y=(1)/(2)x+3` multiply both sides by 2

`2y=2\!\!\!\!\diagup^1\cdot(1)/(2\!\!\!\!\diagup_1)x+(2)(3)`

`2y=x+6` subtract x from both sides

`-x+2y=x-x+6`

`-x+2y=6` change the signs

`x-2y=-6`

2.

`y-2=-(1)/(3)(x+6)` multiply both sides by 3

`3y-(3)(2)=3\!\!\!\!\diagup^1\cdot\left(-(1)/(3\!\!\!\!\diagup_1)\right)(x+6)`

`3y-6=-(x+6)`

`3y-6=-x-6` add 6 to both sides

`3y-6+6=-x-6+6`

`3y=-x` add x to both sides

`x+3y=-x+x`

`x+3y=0`

Answer 2

-x+2y=6 and x+3y=0

Explanation:

Ax+By=C

y=1/2 x+ 3

y= x+6/2

2y=x+6

-x+2y=6------------1

y-2=-1/3(x+6)

3(y-2)= -(x+6)

3y-6=-x-6

3y+x=-6+6

x+3y=0------------2