Question 112877
graph each of the following inequalities on the cartesian plane
2x + y <_ -5 
:
First put it in the general "y="
y <= -2x - 5
:
You can choose the value for x to find y, A good start is x = -3
y = -2(-3) -5
y = +6 - 5
y = +1
:
Then x = +3
y = -2(3) - 5
y = -6 - 5
y = -11
:
This gives y a rather high value, perhaps x = +2 would be better for graphing
y = -2(2) - 5
y = -4 - 5
y = -9
:
From what we have done we can make a table
 x | y
--------
-3 |+1
 0 |-5; I always include x = 0 because it's so easy to know the value of y
+2 |-9
+3 |-11
:
If you plot this on +/-10 x-y graph:
{{{ graph( 300, 200, -10, 10, -10, 10, -2x - 5) }}}
:
Note that x=3 will not be included on our 10 by 10 by graph, choose values that
will keep it on a 10 by 10 graph
:
Remembering that this is an <= inequaltity, shade the area at or below the line on this graph.
:
Has this helped answer your questions?