Question

Sketch the graph of the following inequation in XOY co-ordinate system:

|x + 5| ≤ y

Answer 1

|x + 5| ≤ y

∴ - y ≤ x + 5 ≤ y

∴ - y ≤ x + 5     and x + 5 ≤ y

∴ x + y ≥ - 5    and  x - y ≤ - 5

First we draw the lines AB and AC whose equations are x + y = - 5 and x - y = - 5 respectively.

Line	Equation	Points on the X-axis	Points on the Y-axis	Sign	region
AB	x + y = - 5	A(- 5, 0)	B(0, -5)	≥	origin side of line AB
AC	x - y = - 5	A(-5, 0)	C(0, 5)	≤	non-origin side of line AC

The graph of |x + 5| ≤ y is as below: