Question

svlc algebra 1a - standard (15260)
representing relationships

which statement describes the relationship between x and y?

as x increases, y decreases.

as x increases, y decreases and then increases.

as x increases, y increases and then decreases.

as x increases, y increases.

Explanation:

To determine the relationship between \( x \) and \( y \), we analyze the graph. The graph is a V - shaped graph (like the graph of \( y = |x| \) or a similar absolute - value - type graph). For values of \( x \) to the left of the vertex (the minimum point of the V), as \( x \) increases (moves towards the vertex from the left), \( y \) decreases. For values of \( x \) to the right of the vertex, as \( x \) increases (moves away from the vertex to the right), \( y \) increases. So overall, as \( x \) increases, \( y \) first decreases (when moving from left towards the vertex) and then increases (when moving from the vertex to the right).

Answer:

As \( x \) increases, \( y \) decreases and then increases.