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GRAPHING INEQUALITIES
To review solving inequalities, please click on the link below:
http://www.webmath.com/plotineq.html

Graph the solution to y <
2x + 3.
Just as for number-line inequalities, the first step is to find the "equals" part. For two-variable
linear inequalities, the "equals" part is the graph of the straight line; in this case, that means the
"equals" part is the line y = 2x + 3:
Here the straight line
means the equations is
using the ≤ or ≥
The above illustration has the "or equal to" part (it's just the line) graphed; now the "y less than"
part needs to be graphed. In other words, this is where it is shaded on one side of the line or the
other. Less than is below the line and greater than is above the line. So shade in below the line
for this one:
The graph is shaded down
because the equation is
using the less than or
equal to sign ( ≤ )
And that's all there is to it: the side shaded is the "solution region" they want.

Graph the solution to 2x
– 3y < 6.
First, solve for y:
2x – 3y < 6
–3y < –2x + 6
y > ( 2/3 )x – 2
[Note the flipped inequality sign in the last line. Do not forget to flip the inequality if multiplying or
dividing through by a negative!]
Now, find the "equals" part, which is the line
y = ( 2/3 )x – 2. It looks like this:
But this exercise is what is called a "strict" inequality. That is, it isn't an "or equals to" inequality;
it's only "y greater than". In the case of these linear inequalities, the notation for a strict inequality
is a dashed line. So the border of the solution region actually looks like this:
This line is dotted because
you are strictly using just
the greater than or just the
less than sign ( >,< )
By using a dashed line, the border isn't included in the solution. Since this is a " y greater than"
inequality, I want to shade above the line, so the solution looks like this:
This graph is shaded
upwards because the
equation is using the
greater than or equal to
sign ( ≥ )