Question

How do you graph `y>x-3`?

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 - 3`

`y = -3` or `(0, -3)`

For: `x = 3`

`y = 3 - 3`

`y = 0` or `(3, 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.

We will shade the ???? side of the line.

graph{(x^2+(y+3)^2-0.035)((x-3)^2+y^2-0.035)(y-x+3) = 0 [-10, 10, -5, 5]}

To tansform this into an inequality the boundary line will be dashed because the inequality operator does not contains an "or equal to" clause and therefore the line is not part of the solution set.

We will shade the left side of the line.

graph{(y-x+3) > 0 [-10, 10, -5, 5]}