How would you graph #y > x# and also #2 ≤ x ≤ 6#?

1 Answer
Joe D.
Apr 1, 2015

These kind of problems are solved partially.

First

Shade the area #2 <= x <= 6# on the coordinate plane. It should be an infinitely long rectangle (sides are included).

Second

We should graph #y>x# on the coordinate plane. To do this, we should draw #y =x# first.

Since #y# is not equal to #x#, the line should be dashed, not straight.

Then take a random point that is not on the line #y=x#, for example #A: (1,2)#

If point #A# satisfies the inequality #y>x# we will shade that part of the coordinate plane. Else, we will shade the other part.

When #x=1# and #y=2#, #y>x# satisfied. So we will shade the upper part of the line #y=x# where our random point is included.

Finally

Now there are two different shaded parts on the coordinate plane. The solution is the intersection of these shaded parts. So both inequalities are satisfied.

To see the graph: Graph on QuickMath

If the link doesn't run as expected, write these 3 inequalities to see the graph:
- #y>x#
- #2<=x#
- #x<=6#

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