Question

How do you graph `|y|= 6- |3x|`?

Answer 1

`|y|>=0 to |x|<=2`. Draw the four straight lines `y=+-3x+-6`. The periphery of the so formed rhombus, with vertices at `(+-2, 0) and (0, +-6)`, is the graph for the given equation.

Explanation:

`|y|>=0 to |3x|<=6 to |x|<=2`.

The given equation is the compounded equation for the quadruplet `+-y=6+-3x to y=+-3x+-6`.

These lines, in pairs, meet at `(+-2, 0) and (0, +-6)` and form a rhombus. of side `sqrt40`..

The rhombus reaches the limits `x=+-2`, from within.

Only the coordinates (x, y) of points on this rhombus are governed by the given equation. The rhombus is the graph.