Graphing absolute value equations

To graph an absolute value equation you must know that the parent function in y=|x| and looks like this when graphed; with a slope of 1/1:

The equation for this (and any absolute value equation) is y=a |x-h| + k.
Your vertex for the graph is your (h,k). The h value move the opposite direction, so if it was |x+4| the graph would move to the left 4 instead of right since it is inside the absolute value bars. A tells you if the V (a.k.a. the shape the equation makes when graphed) opens upward or downward. H moves your V left or right and k moves your V up or down.

Systems of Equations

Consistent/ Independent - when two lines intersect at one point on a graph; one solution
Consistent/ Dependent - same slope; same y-intercept; same line; solutions
Inconsistent - parallel; same slope; different y-intercept; no solution