I have a graph which I need to find the equation of. It's an absolute value graph, the vertex/middle point is at (-2, 5) and 2 points that lie on the graph are (1,10) and (-5,10). It needs to be in 'y=' form. I'd appreciate it if you explained how to do find the equation, too.
any linear absolute equation has its "vertex" on the x-axis.
so whatever y = │mx + b│ was must have been translated vertically by 5 units.
so move 2 of the points back down to get
(-2,5) --> (-2,0)
(1,10) --> (1,5)
the slope of this line is 5/3
and its equation is
y = (5/3)x + b
with the point (-2,0) on it
0 = 10/3 + b
b = 10/3
so the equation of the absolute value function with "vertex) at (-2,0) is
y = │ (5/3)x + 10/3 │ , now let's move it up 5 units
y = │ (5/3)x + 10/3 │ + 5
check:
if x = -2, y = │-10/3 + 10/3│ + 5 = 5
x = 1 : y = │15/3│+5 = 10
x = -5 , y = │-25/3 + 10/3│ + 5 = 10