|x| + |y| ≤ 1
What is the region in the plane that solves this inequality?
The Attempt at a Solution
I first tried graphing it by isolating the y variable
|y| ≤ -|x| + 1
Then I looked at the hint we were given, which was to assume that x and y are both positive, so I treated it as if it were written
y ≤ -x+1
And then constructed a graph of a line that was basically y = -x+1 with a domain of [0,3]
But then what threw me off is that the y variable does have the absolute value bars, so there can't be negative y values in the graph, right? So now I'm thinking I just have to flip the part of the graph so that it more closely resembles y=|x-1| in the domain of [0,3]. Is that correct or am I completely missing this?