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

1 Answer
Mar 6, 2016

Answer:

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))#

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

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))#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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)#

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