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graphing linear inequalities

x + 2y > 6

y < -4

graph the system of linear inequalities

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1 Answer

To begin graphing an inequality, you start just like graphing an equation with an = sign.  Your second equation is the easier, so let's start with that.

y< or = -4.  Find y=4, draw across as a solid line (horizontal line to indicate all values of x are valid), and then shade everything under it (i.e., all values of y less than -4) to indicate they are answers too.  Now you are done with that.


The first equation needs to be rearranged to make it easier to graph.  Subtract x from both sides:

2y> -x+6

Divide by 2:

y > (-1/2) x + 3

This is a line with y intercept +3, and slope (-1/2).  You don't have y = (-1/2) x + 3, you have y >(-1/2) x + 3.  So the line you draw can't be solid - those values are not valid.  So you draw the line as dashed.  Then you shade all the values above the dashed line (y bigger than those values) to indicate they are valid.


Keep in mind 2 things:

(1)  For any y=mx+b, you can remember what to do with m and b like so: 

(B)egin the line at b, and

(M)ake the line by following the m (slope) directions, or (M)ove from b according to the m (slope) directions.  Slope directions = (change in y) / (change in x).


(2)  Should  you ever need to multiple or divide an inequality by a NEGATIVE number, you must switch the direction of the inequality.



In the 3rd line:
y< or = -4. Find y=4,
  should be:
y< or = -4. Find y=-4,

OOPS is right!  Thanks Gene!