well, to graph inequalities, what we do is, we graph its EQUALITY counterpart, in this case, we graph the counterpart 6x + y = 5,
6x + y = 5
y = 5 - 6x <--- we graph that, that is the line.
and since it's a ⩾, the line will be a solid line.
for the shading, we do a true/false regions check, let's do that right now
say let's check where the point hmmm 0,0 is at, on what region.
0,0 .............. x = 0, y = 0
y ⩾ 5 - 6x
0 ⩾ 5 - 6(0)
0 ⩾ 5 <---- is that true? is 0 larger or equals to 5? NOT.
that simply means that point is on the false region, so that area we don't shade, so we shade the other side.
check the picture below.