How do you graph #3x+2y>6#?

When inequalities containing two variables, as in the example need to be plotted, we have to temporarily remove the sign of inequality and replace it with an equality sign. This enables us to rearrange the expression so it becomes a function. This is not possible when the inequality sign is present, because variables can represent both positive and negative values and we would not know whether the sign needed reversing after division or multiplication by a factor containing a variable.

Arranging as a function of #x#

#y = -3/2x +3#

We can now plot the line, making sure to use a dashed line to indicate that values on the line are not included since the inequality is not an equal to inequality.

Returning to #3x + 2y > 6#

Check coordinates on each side of the line and see which satisfy

#3x + 2y > 6#

From the left.

#( -2 , 2 )# gives #- 2 > 6# This is false.

From the right.

#( 2 , 2 )# gives #10 > 6# This is true.

The side that satisfies the inequality is the shaded area on the graph, in this case the right side of the line.

See graph:
graph{3x + 2y > 6 [-10, 10, -5, 5]}