Verified answer

You can get the boundary |x| + |y| = 1 (with the equal sign for the boundary of the region) in four pieces.

Quad I: x and y positive, so |x| = x and |y| = y, the equation is x + y = 1

write this as y = 1 - x

This gives the line segment from (1,0) to (0,1) (slope -1 y-intercept 1).

Quad II: x negative and y positive, so |x| = - x and |y| = y, the equation is -x + y = 1

write this as y = 1 + x

This gives the line segment from (-1,0) to (0,1) (slope 1 y-intercept 1).

Quad III: x and y both negative, so |x| = -x and |y| = -y, the equation is -x - y = 1

write this as y = -1 - x

This gives the line segment from (-1,0) to (0,-1) (slope -1 y-intercept -1).

Quad IV: x positive and y negative, so |x| = x and |y| = - y, the equation is x - y = 1

write this as y = -1 + x

This gives the line segment from (1,0) to (0,-1) (slope 1 y-intercept -1).

It looks like a diamond (it a square a.k.a. rhombus with vertices on the axes at (1,0),(0,1),(-1,0), and (0, -1).

The inequality |x| + |y| ≤ 1 gives you the square and its interior.

Here is a pic:

http://www.wolframalpha.com/input/?i=%7Cx%7C+%2B+%...