Question

How do you graph `x+y<0` on the coordinate plane?

Answer 1

See a solution process below:

Explanation:

First, solve for two points as an equation instead of an inequality to find the boundary line for the inequality.

For: `x = 2`

`2 + y = 0`

`2 - color(red)(2) + y = 0 - color(red)(2)`

`0 + y = -2`

`y = -2` or `(2, -2)`

For: `x = 4`

`4 + y = 0`

`4 - color(red)(4) + y = 0 - color(red)(4)`

`0 + y = -4`

`y = -4` or `(4, -4)`

We can now graph the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality.

graph{((x-2)^2+(y+2)^2-0.035)((x-4)^2+(y+4)^2-0.035)(x+y)=0 [-10, 10, -5, 5]}

Now, we can shade the left side of the line.

However, we need to change the boundary line to a dashed line because the inequality operator does not contain an "or equal to" clause.

graph{(x+y) < 0 [-10, 10, -5, 5]}