The graph provided shows a V-shaped absolute value function, which is characteristic of absolute value equations. From the options given, the task is to identify the correct equation for this graph.

Let’s break down the characteristics of the graph:

1. Vertex of the graph: The vertex of the V-shaped graph appears to be at the point $(5, 2)$.

2. Standard form of an absolute value function: The general form is $y = a|x - h| + k$, where:

   • $(h, k)$ is the vertex of the graph.
   • $a$ controls the direction and steepness of the graph (if $a$ is negative, the graph opens downward, otherwise it opens upward).

3. Equation analysis: Based on the graph:

   • The vertex is $(5, 2)$, so we expect the equation to be in the form $y - 2 = |x - 5|$.

Given this, the correct equation from the choices is: $y - 2 = |x - 5|$

This is the correct equation for the graph.

Do you want further details or have any questions?

Here are 5 related questions for deeper understanding:

1. How does changing the vertex $(h, k)$ affect the absolute value graph?
2. What happens to the graph if the coefficient $a$ is negative?
3. How do you solve an equation involving absolute values?
4. What role does the absolute value play in reflecting part of the graph?
5. Can you graph an absolute value equation by hand using a table of values?

Tip: When working with absolute value functions, always check the vertex and the direction of the "V" shape to help identify the correct equation.