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

Apr 10, 2016

$| y | \ge 0 \to | x | \le 2$. Draw the four straight lines $y = \pm 3 x \pm 6$. The periphery of the so formed rhombus, with vertices at $\left(\pm 2 , 0\right) \mathmr{and} \left(0 , \pm 6\right)$, is the graph for the given equation.

#### Explanation:

$| y | \ge 0 \to | 3 x | \le 6 \to | x | \le 2$.

The given equation is the compounded equation for the quadruplet $\pm y = 6 \pm 3 x \to y = \pm 3 x \pm 6$.

These lines, in pairs, meet at $\left(\pm 2 , 0\right) \mathmr{and} \left(0 , \pm 6\right)$ and form a rhombus. of side $\sqrt{40}$..

The rhombus reaches the limits $x = \pm 2$, from within.

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