Question

How do you graph `x+y<-4`?

Answer 1

See explanation

Note: if the inequality had been `x+y<=-4` you would have used a solid line.

Explanation:

Although not the case, just for now consider it as `x+y=-4` to determine the line to be graphed.

Subtract `x` from both sides

`y=-x-4`

This will plot the line. However what we really have is:

`x+y<-44`

Subtract `x` from both sides

`y<-x-4`

As `y` is 'less than' something done to `x`, the value of `y` can never actually be the value on the line. Consequently we use a dotted line to signify this condition. You would also use a dotted line for greater than.

To indicate that `y` can take on any value less then the line the area under the line (less than) is shaded.

So we have: