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

1 Answer
Mar 6, 2016

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 BTony B