Question

How do you graph the inequality `2x+y< -3`?

Answer 1

See a solution process below:

Explanation:

First calculate two points on the line for this as an equation instead of an inequality to find the border of the inequality:

For `x = 0`: `(2 xx 0) + y = -3`

`0 + y = -3`

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

For `x = -3`: `(2 xx -3) + y = -3`

`-6 + y = -3`

`color(red)(6) - 6 + y = color(red)(6) - 3`

`0 + y = 3`

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

We can now plot these two points and draw a line through them to find the border of the inequality:

graph{(x^2+(y+3)^2-0.05)((x+3)^2+(y-3)^2-0.05)(2x+y+3)=0}

Now that we have the border we can chart the inequality. Because the inequality operator contains a "or equal to" clause it will stay as a solid line. And because it has a "less than" clause we will shade to the left of the line:

graph{(2x+y+3)<=0}