y > 
x - 2
First we draw the boundary line, which has an equation
just like the inequality, but which has an equal sign
in place of the >
y = x - 2
We graph that line either by using the y-intercept and the slope,
or by finding two points. If she doesn't know how to graph a line
then post again asking how.
We'll draw that line dotted, not solid, because the inequality is
>, not ≥, and does not include the boundary line:
All of the solutions to the original inequality y > x - 2
are one one side of that line, but we don't know which side. So we
use an arbitrary test point which is not on the line. The easiest
test point to choose is the point (0,0), the origin. So we substitute
x=0 and y=0 into the original inequality and see if it is true or
false:
y > x - 2
0 > (0) - 2
0 > 0 - 2
0 > -2
That is true since zero is greater than any negative number.
Therefore since (0,0) is a solution, all the points on the same
side of the line that (0,0) is on are also solutions. Since
(0,0), the origin, is on the upper side of the line, that's
the side we shade:
Edwin
