6.5  Graphing Linear Inequalities in Two Variables

Mrs. Agriesti's Algebra

Goal: To graph linear inequalities in two variables.

Example 1:     Sketch the graph of y < 4.

See section 4.1 for help graphing the line.  Use a dashed line since there is no =. 

Choose a point that is not on the line and test it to see if it is a solution.  (Plug the x-coordinate and the y-coordinate into the inequality and see if it makes a true statement.)  The easiest point to use is the origin (0, 0). 

Is 0 < 4? 

Yes it is  - shade on the side with the origin.

Example 2:     Sketch the graph of 6x + 5y > 30.

See section 4.3 for help graphing the line.  The intercepts are (0, 6) and (5, 0).  Use a solid line this time since there is an =. 

Choose a point that is not on the line and test it to see if it is a solution.  I would use the origin (0, 0) again. 

Is 6(0) + 5(0) > 30?
     0    +   0   > 30?   no!

Shade on the other side of the line (not the side with the origin).

Example 3:     Sketch the graph of y > 3x.

See section 4.5 for help graphing the line.  The y-intercept is 0 and the slope is 3.  Use a dashed line this time since there is no =. 

Choose a point that is not on the line and test it to see if it is a solution.  This time the origin is on the line so you can't use it.  I'm going to use the point (1, 1) instead.   

Is 1 > 3(1) ?
   1  > 3 ?   no!

Shade on the other side of the line (not the side that the point (1,1) is on).