Question

How do you graph the inequality `x + y <6`?

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 = 6`

`y = 6` or `(0, 6)`

For: `y = 0`

`x + 0 = 6`

`x = 6` or `(6, 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.

graph{(x^2+(y-6)^2-0.125)((x-6)^2+y^2-0.125)(x+y-6)=0 [-20, 20, -10, 10]}

Now, we can shade the left side 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-6) < 0 [-20, 20, -10, 10]}