Question

Write an inequality for the graph?

Answer 1

You want to write an absolute value inequality of the form

\(y \ge a|x - h| + k\) where \((h,k)\) is the vertex of the absolute value graph.

Answer 2

In this case the vertex is (5,1)

Answer 3

To find the value of a, simply use a point that is on the graph of the absolute value lines such as (x,y) = (0,6), then plug the point in to the inequality and solve for a

Answer 4

\(6 = a|0 - 5| + 1\)
\(6 = 5a + 1\)
\(5 = 5a\)
\(a = 1\)

So the inequality that corresponds with the graph is \(y \ge |x - 5| + 1\)