Question

How do you graph the inequality `4x+y> -4`?

Answer 1

See below:

Explanation:

First let's find the equation of the line we'll be using, then we can deal with the inequality.

`4x+y=-4`

Let's put this into slope intercept form:

`y=-4x-4`

The graph of that line looks like this:

graph{-4x-4}

Now to determine what side to shade. I like to do this by seeing if the origin, `(0,0)`, is part of the solution:

`4x+y> -4`

`4(0)+0> -4=>0> -4 color(white)(000)color(green)root`

So we'll shade the origin side (because it made our statement true):

graph{y+4x+4>0}

Notice our line in this graph is dotted - it indicates that the points on the graph are not part of the solution.