First you have to put the equation in slope intercept form:
y=mx+b
x+3y ≤ 6
Isolate y by performing the opposite opperation of subtracting x on both sides of the equation
3y ≤ -x + 6
Divide by 3
y ≤ -1/3x +2
TO graph this, plot your y intercept, which is b in the slope intercept formula. So, plot 2 on the y axis. To plot other points, use the slope. -1/3. Slope is rise over run. So, since the slope is negative, the line will go down instead of up.
So, from (0,4) where you plotted your y int., go down one line on the y axis (rise, or in this case, fall) and to the right 3 lines (run) which you will count on the x axis
Then, plot that point. Continue doing so until you have a decent amount of points
For shading, it is going to be a solid line and everything above your line is going to be shaded because the inequality states that y GREATER THAN or equal to, so everything greater then y needs to be shaded
Hope I explained ok. It's kinda hard to explain graphing when not in person
