Question 206915
{{{graph(300,200, -10, 10, -10, 10, x<3, y>=x)}}}

There is the graph.  But let's solve this LOGICALLY.

What I usually do is I forget about the inequality notations/signs, and say to myself: "what would this graph look like NORMALLY, when x=3, or y=x?"  

Well, then I know for a fact that y=x just comes down on the graph SLANTED.  Well, what does that mean?  WHERE does it slant?

Plug in values for x and y to find out.  

if...

x=1, y=1  

The ordered pair (1,1) comes out.

if...

x=-5, then y=-5

The ordered pair (-5,-5) comes out.

I usually pick up to 5 VALUES of ordered pairs, then just play connect the dots.  Now I know where it slants!  (see graph)



Let's try x<3.  Well, what does it look like if x = 3?  I now find out 3 is a CONSTANT, so when graphed, I go right (because, 3 is positive) 3 on the x axis, and get a straight line, vertical..

Because, x = 3, x IS 3, so 3 right is a vertical line!

As I add the inequalities in, this tells me where the ordered pairs are okay to be (viable).  

Well, how do I know where to shade?  Pick a point not on the line for each equation.

y>or=x;

I'll pick 9,2 for example.  This point (9,2) is NOT on the line.

9 is x; 2 is y.

is 2>or=9;  NO!  So, if 9,2 is close to the RIGHT of the graph, I SHADE opposite.  Because all of that AREA isn't true.  I shade to the left, as depicted on the graph.

Now, x<3.  This is an easy one.  It is saying "the x-values (x's) are LESS THAN (smaller) 3, so smaller values of three are to the LEFT; and we shade left, as depicted on the graph.

And that's it.

e-mail for more help!

Thanks :)