Answer:
1. x - 2y = -6
2. x + 3y = 0
Step-by-step explanation:
The Standard form of an eqaution of a line:
[tex]Ax+By=C[/tex]
1.
[tex]y=\dfrac{1}{2}x+3[/tex] multiply both sides by 2
[tex]2y=2\!\!\!\!\diagup^1\cdot\dfrac{1}{2\!\!\!\!\diagup_1}x+(2)(3)[/tex]
[tex]2y=x+6[/tex] subtract x from both sides
[tex]-x+2y=x-x+6[/tex]
[tex]-x+2y=6[/tex] change the signs
[tex]x-2y=-6[/tex]
2.
[tex]y-2=-\dfrac{1}{3}(x+6)[/tex] multiply both sides by 3
[tex]3y-(3)(2)=3\!\!\!\!\diagup^1\cdot\left(-\dfrac{1}{3\!\!\!\!\diagup_1}\right)(x+6)[/tex]
[tex]3y-6=-(x+6)[/tex]
[tex]3y-6=-x-6[/tex] add 6 to both sides
[tex]3y-6+6=-x-6+6[/tex]
[tex]3y=-x[/tex] add x to both sides
[tex]x+3y=-x+x[/tex]
[tex]x+3y=0[/tex]
