Question

How do you graph the inequality `y ≥ x - 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`

`y = 0 - 1`

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

For: `x = 5`

`y = 5 - 1`

`y = 4` or `(5, 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.
The boundary line will be solid because the inequality operator contains a "or equal to" clause.

graph{(x^2+(y+1)^2-0.125)((x-5)^2+(y-4)^2-0.125)(y-x+1)=0 [-20, 20, -10, 10]}

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

graph{(y-x+1)>=0 [-20, 20, -10, 10]}