Question 598795
The line {{{-2x-3y=6}}} is indeed the line that passes through points (-3,0) and (0,-2).
{{{drawing(300,300,-5,5,-5,5,
grid(1),
circle(-3,0,0.2),circle(0,-2,0.2),
line(-5,4/3,5,-16/3)
)}}}
The inequality {{{-2x-3y<=6}}} includes all the points on that line, where {{{-2x-3y=6}}} , so the line is graphed as a solid line to indicate that.
If the inequality was {{{-2x-3y<6}}} , the line would be dashed to indicate that the line is not part of the solution.
To see what side of the line should be shaded, I always try to use a "test point" that makes my calculations easy. In this case, I would use the point (0,0). I would ask myself "Is (0,0) part of the solution?"
{{{-2*0-3*0=0<6}}} , so (0,0) is part of the solution.
With the line graphed, I notice that (0,0) is above the line, so I would shade the region above the line.
{{{graph(300,300,-5,5,-5,5,-2x-3y<=6)}}}