Question 1200320
<pre>
{{{-2y}}}{{{""=""}}}{{{x+6}}}

First get the equation in slope-intercept form, y = mx + b, by
solving for y

Give x the coefficient 1
{{{-2y}}}{{{""=""}}}{{{1*x+6}}}

Divide through by -2

{{{(-2y)/(-2)}}}{{{""=""}}}{{{expr(1/(-2))*x+6/(-2)}}}

{{{y}}}{{{""=""}}}{{{-expr(1/2)*x-3}}}

Comparing that to y = mx + b we see that the slope m is {{{-1/2}}},
and the y-intercept b is -3.

We plot the y-intercept at -3 on the y-axis:

{{{drawing(400,400,-10,10,-10,10, graph(400,400,-10,10,-10,10), 

circle(0,-3,.02),circle(0,-3,.05),circle(0,-3,.08),circle(0,-3,.1),circle(0,-3,.15)
)}}}

Begin by looking at the numerator and sign of the slope.  The slope is {{{-1/2}}}. 
Its numerator is 1, and its sign is -

Since the sign of the slope is NEGATIVE, we draw a line DOWNWARD from the 
y-intercept. It's the vertical blue line below.

[If the sign of the slope had been POSITIVE we would have drawn a line UPWARD].  

{{{drawing(400,400,-10,10,-10,10, graph(400,400,-10,10,-10,10), 
blue(line(0,-3,0,-4)),
circle(0,-3,.02),circle(0,-3,.05),circle(0,-3,.08),circle(0,-3,.1),circle(0,-3,.15)
)}}}

Next, we look at the denominator of the slope.  The slope is {{{-1/2}}}. Its
denominator is 2.  We always go to the RIGHT with the denominator.  So from
the bottom of the blue line we draw a horizontal line to the right 2 units:

{{{drawing(400,400,-10,10,-10,10, graph(400,400,-10,10,-10,10), 
blue(line(0,-3,0,-4),line(0,-4,2,-4)),
circle(0,-3,.02),circle(0,-3,.05),circle(0,-3,.08),circle(0,-3,.1),circle(0,-3,.15),

circle(2,-4,.02),circle(2,-4,.05),circle(2,-4,.08),circle(2,-4,.1),circle(2,-4,.15)

)}}}

Now we take a straight edge and draw a line through the point where we started,
at the y-intercept, and through the point where we ended up.

{{{drawing(400,400,-10,10,-10,10, graph(400,400,-10,10,-10,10), 
blue(line(0,-3,0,-4),line(0,-4,2,-4)),
circle(0,-3,.02),circle(0,-3,.05),circle(0,-3,.08),circle(0,-3,.1),circle(0,-3,.15),
line(16,-11,-16,5),
circle(2,-4,.02),circle(2,-4,.05),circle(2,-4,.08),circle(2,-4,.1),circle(2,-4,.15)

)}}}
Edwin</pre>