Question

Please help me with this.

Answer 1

Answer:

1. x - 2y = -6

2. x + 3y = 0

Step-by-step explanation:

The Standard form of an eqaution of a line:

$Ax+By=C$

1.

$y=\dfrac{1}{2}x+3$           multiply both sides by 2

$2y=2\!\!\!\!\diagup^1\cdot\dfrac{1}{2\!\!\!\!\diagup_1}x+(2)(3)$

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

$-x+2y=x-x+6$

$-x+2y=6$           change the signs

$x-2y=-6$

2.

$y-2=-\dfrac{1}{3}(x+6)$           multiply both sides by 3

$3y-(3)(2)=3\!\!\!\!\diagup^1\cdot\left(-\dfrac{1}{3\!\!\!\!\diagup_1}\right)(x+6)$

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

$3y-6=-x-6$            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

Answer:

-x+2y=6   and   x+3y=0

Step-by-step 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