Question

How do you graph the inequality `x+y>1`?

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 = 0`

`0 + y = 1`

`y = 1` or `(0, 1)`

For: `y = 0`

`x + 0 = 1`

`x = 1` or `(1, 0)`

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.
The boundary line will be solid because the inequality operator contains an "or equal to" clause.

graph{(x^2+(y-1)^2-0.05)((x-1)^2+y^2-0.05)(x+y-1)=0 [-10, 10, -5, 5]}

Now, we can shade the rightside of the line.

The boundary line will be changed to a dashed line because the inequality operator does not contain an "or equal to" clause.

graph{(x+y-1) > 0 [-10, 10, -5, 5]}