Question

How do you graph `x-5<=y`?

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 - 5 = y`

`-5 = y`

`y = -5` or `(0, -5)`

For: `x = 5`

`5 - 5 = y`

`0 = y`

`y = 0` or `(5, 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+5)^2-0.125)((x-5)^2+y^2-0.125)(y-x+5)=0 [-20, 20, -10, 10]}

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

graph{(y-x+5) >=0 [-20, 20, -10, 10]}