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

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

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Answer 1 · 2016-03-06T21:23:41

See the explanation about method.

Explanation:

Build a table for $y = x + 5$ $y=x+5$ but make all values for $y$ $y$ 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 $x = 0$ $x=0$ so $y = | 0 + 5 | = 5$ $y=|0+5|=5$

$Thus the first point P_{1} \to (x_{1}, y_{1}) \to (0, 5)$ $color(blue)("Thus the first point "P_1->(x_1,y_1)->(0,5))$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The x-intercept is at $y = 0$ $y=0$

$y = 0 = x + 5 \to 0 = - x + 5$ $y=0=x+5" "->" "0=-x+5$

Add $x$ $x$ to both sides $0 + x = - x + x + 5 \Rightarrow x = 0 + 5$ $0+x=-x+x+5" "=>" "x=0+5$

$Thus the second point P_{2} \to (x_{2}, y_{2}) \to (5, 0)$ $color(blue)("Thus the second point "P_2" "->" "(x_2,y_2)" "->" "(5,0))$
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The third point will be a reflection of the first point about the axis of symmetry of $x = 5$ $x=5$ thus completing the V shape

So the x-coordinate will be $x_{2} + (x_{2} - x_{1}) = 5 + 5 = 10$ $x_2+(x_2-x_1) = 5+5=10$
The y coordinate will be the same as $y_{1}$ $y_1$

$Thus the third point P_{3} \to (x_{3}, y_{3}) \to (10, 5)$ $color(blue)("Thus the third point "P_3" "->" "(x_3,y_3)" "->" "(10,5)$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Both of these plotted lines will be extended upwards to the edge of the graph.
Tony B Tony B

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

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