SOLUTION: PLease help to graph y < 2 5x + 3y

SOLUTION: PLease help to graph y < 2 5x + 3y > or equal to 12

Question 66660: PLease help to graph
y < 2
5x + 3y > or equal to 12
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
y < 2
This isjust a horizontal line going thru +2 on the y axis, < 2 means the area of interest is below the line and not at the line
5x + 3y >= 12
Arrange the equation in the general "y=" form
:
3y >= 12 - 5x
y >= 12/3 - (5/3)x
y >= 4 - (5/3)x
:
Make a table of x values and the corresponding value for y:
An example for x = -3:
y = 4 - (5/3)(-3)
y = 4 + 5; a minus a minus is a plus, the 3's cancel
y = +9 when x = -3
:
x | y
------
-3| 9
0 | 4
+3|-1
Notice I picked some values which avoided the use of fractions, but this OK because it is a straight line and easy to plot this way.
:
Your graph should look like this:

:
Notice our equation says y => 4 - (5/3)x, this means the area of interest is at and above the green line in the graph.
:
However, the y < 2 means it is below the red line, so the area bounded by these two equations would the triangular area at/above and to the right of the green line and below the red line. Does this make sense to you?
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