Which system of inequalities is represented by the graph

y ≤ 2x + 4 and x + y ≥ -6

Step-by-step explanation:

Graphing a system of inequalities is similar to graphing linear functions.  It is best to have equations in the form of y = mx + b where m = slope and b = y-intercept.  Looking at the graph, you can see that there is one line going uphill (positive slope) and one going downhill (negative slope).  There are two y-intercepts, one from each line at (0,4) and (0, -6)  So, only the top two equations have a y-intercept equal to 4 and -6.  Then, you can find the slope of each line by choosing two points on the same line and using rise/run to find the change in 'y' over the change in 'x'.  

Line #1 (uphill):  (-2, 0) and (0, 4) = 4-0/0- -2 = 4/2 = 2

The only answer with a positve 2 slope and y-intercepts of 4 and -6 is the second one, so that is your answer.