Question 114699
The slope intercept form is {{{y=mx+b}}} where m is the slope and b is the y-intercept.

To be parallel the line must have the same slope.

Transposing x=2y+12 to slope-intercept,

{{{x=2y+12}}}
{{{2y+12=x}}}
{{{2y+12-12=x-12}}}
{{{2y+0=x-12}}}
{{{2y=x-12}}}
{{{2y/2=(x-12)/2}}}
{{{y=x/2-6}}}

Here, {{{m=1/2}}}


Now, we must find a line that passes through (0,6) and has a slope of {{{1/2}}}.

Since the line passes through (0,6), we will use x=0 and y=6

{{{y=mx+b}}}
{{{0=(1/2)(6)+b}}} --------------i used {{{m=1/2}}}
{{{0=3+b}}}
{{{b=-3}}}

Now, we know that b=-3. So,
{{{y=x/2+(-3)}}}
{{{y=x/2-3}}}
This is the equation of the line. Proof? Look below!

{{{graph(1000,1000,-20,20,-20,20,x/2-3,x/2-6)}}}


They are parallel!


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