There are a couple possible approaches. Here's one.
I finding leading negative signs hard to read, so I would begin by rewriting the inequality as: 3x-y <= 63x−y≤6
Start by graphing the equation: 3x-y = 63x−y=6
For this equation, it is straightforward to find the intercepts, so that's now I would graph this one.
(If you prefer to put it in slope-intercept form first, do that.)
(0, -6)(0,−6) and (2, 0)(2,0) are the intercepts so draw the line through those two points. So you get this:
graph{3x-y = 6 [-10, 10, -5, 5]}
The line 3x-y = 63x−y=6 cuts the plane into two regions. In one region, the value of 3x-y3x−y is <6<6, in the other it is >6>6. Our job now is to figure out which side is which so we can stay on the "less than 6" side.
I see that the point (0,0)(0,0) (the origin) is not on the graph of the equation, so I'll just check to see if that side is the <6<6 or >6>6 side.
3(0)-(0)=0-0=03(0)−(0)=0−0=0 which is less than 66. So the region above the line must be the <6<6 side of the line.
The inequality we're looking at wants the <=6≤6 side, so we shade that side. (If you wanted to double check, you could pick a point above the line. Say (5, 0)(5,0) or (10, 0) and make sure that andmakesuretˆ3x - y < 6#
Your graph should look like this:
graph{3x-y<=6 [-10, 10, -5, 5]}
