Answer
Please see the graph.
Work Step by Step
Blue line: $2x+4y<6$
Green line: $y\le-4$
Let's use the point $(0,0)$ to determine what sides of the lines to shade.
Blue line: $2x+4y<6$
$2x+4y<6$
$2*0+4*0<6$
$0+0 < 6$
$0 < 6$ (true)
Since this is true, then we will shade the side of the line with the point. We have a "less than" sign, so we'll use a dotted line to shade.
Green line: $y\le-4$
$y\le-4$
$0 \le -4$ (false)
Since this is false, then we will shade the side of the line without the point. We have a "less than or equal to" sign, so we'll use a solid line to shade.
We want the intersection of the two graphs, so the intersection of the two graphs is the area of the graph that is green and blue.
