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

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

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Answer 1 · 2016-04-10T12:41:35

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

Explanation:

$| y | \geq 0 \to | 3 x | \leq 6 \to | x | \leq 2$ $|y|>=0 to |3x|<=6 to |x|<=2$ .

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

These lines, in pairs, meet at $(\pm 2, 0) and (0, \pm 6)$ $(+-2, 0) and (0, +-6)$ and form a rhombus. of side $\sqrt{40}$ $sqrt40$ ..

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

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

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

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