Question 300000
{{{7x+6y<=-18}}}
<pre><font size = 4 color = "indigo"><b>
Graph the boundary line which has the equation which
is just like the inequality but has an equal sign
where the inequality has a {{{""<=""}}} sign.

Equation of boundary line: {{{7x+6y=-18}}}

Get some points on that line. I choose values of x that 
will divide evenly into 6 and 18, so that I get whole
numbers but you can plot fractions in between the integers:

 x |  y 
-6 |  4
 0 | -3
 6 |-10

Plot those points:

{{{drawing(400,400,-12,12,-12,12,
graph(400,400,-12,12,-12,12),
line(-6+.1,4,-6-.1,4), line(-6,4+.1,-6,4-.1),
line(-6+.1,4+.1,-6-.1,4-.1), line(-6+.1,4-.1,-6-.1,4+.1),
line(0+.1,-3,0-.1,-3), line(0,-3+.1,0,-3-.1),
line(0+.1,-3+.1,0-.1,-3-.1), line(0+.1,-3-.1,0-.1,-3+.1),
line(6+.1,-10,6-.1,-10), line(6,-10+.1,6,-10-.1),
line(6+.1,-10+.1,6-.1,-10-.1), line(6+.1,-10-.1,6-.1,-10+.1)

  )}}}

Draw the boundary line through them:

{{{drawing(400,400,-12,12,-12,12,
graph(400,400,-12,12,-12,12),
line(-6+.1,4,-6-.1,4), line(-6,4+.1,-6,4-.1),
line(-6+.1,4+.1,-6-.1,4-.1), line(-6+.1,4-.1,-6-.1,4+.1),
line(0+.1,-3,0-.1,-3), line(0,-3+.1,0,-3-.1),
line(0+.1,-3+.1,0-.1,-3-.1), line(0+.1,-3-.1,0-.1,-3+.1),
line(6+.1,-10,6-.1,-10), line(6,-10+.1,6,-10-.1),
line(6+.1,-10+.1,6-.1,-10-.1), line(6+.1,-10-.1,6-.1,-10+.1),
green(line(-12,11,12,-17))
  )}}} 

All of the points on one side of the green line represent solutions
to the original inequality.  To find out which side they are all
on, we pick any point on either side of the line, but NOT ON
the line and test it in the original inequality.  Let's pick
the origin (x,y) = (0,0) since it is easy and it is NOT ON the 
line.  

Substitute 0 for x and 0 for y

{{{7x+6y<=-18}}}
{{{7(0)+6(0)<=-18}}}
{{{0<=-18}}}

That is false.  Therefore the origin is on the side where the
solutions are NOT on, so we shade the side of the green line
which the origin is NOT on.  The origin is on the upper right
side of the green line, so we will shade the lower left side
of the green line.

I can't shade on here but you can on your paper.  

{{{drawing(400,400,-12,12,-12,12,
graph(400,400,-12,12,-12,12),
line(-6+.1,4,-6-.1,4), line(-6,4+.1,-6,4-.1),
line(-6+.1,4+.1,-6-.1,4-.1), line(-6+.1,4-.1,-6-.1,4+.1),
line(0+.1,-3,0-.1,-3), line(0,-3+.1,0,-3-.1),
line(0+.1,-3+.1,0-.1,-3-.1), line(0+.1,-3-.1,0-.1,-3+.1),
line(6+.1,-10,6-.1,-10), line(6,-10+.1,6,-10-.1),
line(6+.1,-10+.1,6-.1,-10-.1), line(6+.1,-10-.1,6-.1,-10+.1),
green(line(-12,11,12,-17)), locate(-12,-5, "SHADE_THIS_SIDE_OF_THE_LINE"), 
locate(-12,5,"SHADE_THIS"),locate(-12,3.5,"SIDE_OF_LINE"), 
locate(-9,-9, "SHADE_THIS_SIDE_OF_THE_LINE") 
 )}}} 


Edwin</pre>