Graph the inequality.
2x + 3y > 6
First draw the graph of the boundary line,
whose equation is same as the inequality
with and equal sign replacing the " > ".
We get two points. The two intercepts are the
easiest to get (0,2) and (3,0). Then we plot
those and draw a dotted line through them.
Now we must decide which side of the dotted line to
shade, by these rules.
1. If the coefficient of x is positive:
A. Shade the side to the right the line if the inequality is
either ">" or ">
B. Shade the side to the left of the line if the inequality is
either "<" or "<
2. If the coefficient of x is negative:
A. Shade the side to the left of the line if the inequality is
either ">" or ">
B. Shade the side to the right of the line if the inequality is
either "<" or "<
3. If the coefficient of y is positive:
A. Shade the upper side of the line if the inequality is
either ">" or ">
B. Shade the lower side of the line if the inequality is
either "<" or "<
4. If the coefficient of y is negative:
A. Shade the lower side of the line if the inequality is
either ">" or ">
B. Shade the upper side of the line if the inequality is
either "<" or "<
2x + 3y > 6
In this case, both coefficients are positive and the inequality
is " > ", so both 1.A. and 3.A. apply so we shade the side which
is both above and to the right side of the line.
Edwin
