Question

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

Answer 1

See the explanation about method.

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`

`color(blue)("Thus the first point "P_1->(x_1,y_1)->(0,5))`

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The x-intercept is at `y=0`

`y=0=x+5" "->" "0=-x+5`

Add `x` to both sides `0+x=-x+x+5" "=>" "x=0+5`

`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` thus completing the V shape

So the x-coordinate will be `x_2+(x_2-x_1) = 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.