Question 1087317
The linear inequality divides the coordinate plane into two halves by a boundary line (the line that corresponds to the function). One side of the {{{boundary}}} line contains all solutions to the inequality.

The {{{boundary}}} line is {{{dashed}}} for > and < and {{{solid}}} for &#8805; and &#8804;.

you have:

{{{x+2y <= 4}}}.....solve for {{{y}}}

{{{2y <=-x+ 4}}}

{{{y <=-x/2+ 4/2}}}

{{{y <=-x/2+ 2}}}

{{{ graph( 600, 600, -10, 10, -10, 10, y <=-x/2+ 2,-x/2+ 2,-x/2+ 2) }}}


The red colored area, the area on the plane that contains all possible solutions to your inequality, and it is called the {{{bounded}}} {{{region}}}. 

The green line that marks the edge of the bounded area is very logically called the {{{boundary}}} {{{line}}} and in your case it is a {{{solid}}}  line {{{y =-x/2+ 2}}} . 
In this case, all points on the line do satisfy the inequality.
 
If they didn’t, the boundary line would be dashed and the inequality the inequality would be {{{y <-x/2+ 2}}}.