Answer:
a = -2/9
Step-by-step explanation:
Locate two points that cross grid intersections and compute the slope of the line between them. I would choose the vertex (4, 4) and the point (-5, 2) as being points where the graph crosses grid intersections.
The slope of the line between those points is given by the slope formula ...
m = (y2 -y1)/(x2 -x1)
m = (2 -4)/(-5 -4) = -2/-9 = 2/9
We note that this representation of the absolute value function appears inverted (reflected across the x-axis). That means the coefficient 'a' will be negative. The slope of an unmodified absolute value function is -1 to the left of the vertex. It will only be 2/9 if the function has been multiplied by -2/9.
a = -2/9
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Additional comment
The vertex on the graph is at (4, 4), so the values of (h, k) are (4, 4).
