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

Apr 22, 2016

See explanantion

#### Explanation:

Write out a table for different values of $x$. If the answer is such that y is negative change the answer to positive. That is what the two vertical lines mean. This answer is always positive.

This means that the graph is of general shape $\vee$.

$\textcolor{b l u e}{\text{Determine where the slope changes from negative to positive.}}$

Write as $y = 3 | x + 2 |$

Set y to 0 giving

$0 = 3 | x + 2 |$

Divide both sides by 3

$0 = | x + 2 |$

$\implies x = - 2$

So the point of the $\textcolor{b l u e}{\text{vertex} \to \left(x , y\right) \to \left(- 2 , 0\right)}$
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We only $\underline{\text{need two more points}}$ and you can plot your graph.

I chose one of them to be $x = - 3$

So $y = | 3 \left(- 3\right) + 6 |$

$y = | - 9 + 6 |$

$y = | - 3 |$

$y = + 3$

$\textcolor{b l u e}{\text{So one point is } \left(x , y\right) \to \left(- 3 , + 3\right)}$
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I will let you determine the other one.

Apr 22, 2016

$y \ge 0$. Draw the straight lines y = 3 x + 6 that passes through $\left(0 , 6\right) \mathmr{and} \left(- 2 , 0\right) \mathmr{and} y = - \left(3 x + 6\right)$ that passes through $\left(0 , - 6\right) \mathmr{and} \left(- 2 , 0\right)$. Graph is V-like half of the pair, above the x-axis.

#### Explanation:

$y = | 3 x + 6 |$ is the combined equation for the pair of lines $y = \pm \left(3 x + 6\right)$, subject to the condition $y \ge 0$.

These two lines cut at $\left(- 2 , 0\right)$

The V-like part of the pair of lines from and above the point of intersection $\left(- 2 , 0\right)$ makes the graph.