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 = 3`

`y = 3/3`

`y = 1` or `(3, 1)`

For: `x = 6`

`y = 6/3`

`y = 2` or `(6, 2)`

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-3)^2+(y-1)^2-0.05)((x-6)^2+(y-2)^2-0.05)(y-(x/3))=0 [-10, 10, -5, 5]}

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

We also need to change the boundary line to be a dashed line because the inequality operator does not contain an "or equal to" clause.

graph{(y-(x/3)) < 0 [-10, 10, -5, 5]}