Question

How do you graph the inequality `2x + 3y> 6`?

Answer 1

Draw a dashed line and shade above the line.

Explanation:

Draw the straight line graph of `2x +3y =6`

Use the intercept method:

For the `x-`intercept, make `y=0 rarr 2x = 6 rarr x= 3`

For the `y-`intercept, make `x=0 rarr 3y = 6 rarr y= 2`

Now that you have the two intercepts you can draw the line.
However because the inequality sign `>` is used, the line itself is not part of the solution, draw a dashed line, not a solid line.

To show the solution, you need to shade one side of the line.
In this case shade the wanted region.

To decide which side, test with the origin `(0,0)`

`2x +3y > 6`
`2(0) +3(0) > 6`

`0 > 0` is false, so `(0,0)` is NOT part of the solution.

Shade the area which does NOT include the origin.
(ie shade above the line) for the solution/