# How do you graph y = |x+5|?

Mar 6, 2016

#### Explanation:

Build a table for $y = x + 5$ but make all values for $y$ positive

Use this table to plot points. However; this is a plot involving two straight lines that make a V shape. So, in theory you only need 3 points.

The y-intercept is at $x = 0$ so $y = | 0 + 5 | = 5$

$\textcolor{b l u e}{\text{Thus the first point } {P}_{1} \to \left({x}_{1} , {y}_{1}\right) \to \left(0 , 5\right)}$

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The x-intercept is at $y = 0$

$y = 0 = x + 5 \text{ "->" } 0 = - x + 5$

Add $x$ to both sides $0 + x = - x + x + 5 \text{ "=>" } x = 0 + 5$

$\textcolor{b l u e}{\text{Thus the second point "P_2" "->" "(x_2,y_2)" "->" } \left(5 , 0\right)}$
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The third point will be a reflection of the first point about the axis of symmetry of $x = 5$ thus completing the V shape

So the x-coordinate will be ${x}_{2} + \left({x}_{2} - {x}_{1}\right) = 5 + 5 = 10$
The y coordinate will be the same as ${y}_{1}$

color(blue)("Thus the third point "P_3" "->" "(x_3,y_3)" "->" "(10,5)

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Both of these plotted lines will be extended upwards to the edge of the graph.