Question

which graph represents a function with direct variation? (graphs are shown with coordinate planes and lines; first graph has a line crossing y-axis at -2, second at 3)

Explanation:

Step1: Recall Direct Variation Definition

A direct variation function has the form \( y = kx \), where \( k \) is a constant. Its graph is a straight line passing through the origin \((0,0)\).

Step2: Analyze Each Graph

• First graph: The line intersects the \( y \)-axis at \( y = -2 \) (not the origin), so it's not direct variation.
• Second graph: The line passes through the origin \((0,0)\), matching the form \( y = kx \) for direct variation.

Answer:

The Middle Graph (assuming the second graph is the middle one, but based on the description, the graph passing through the origin is the one representing direct variation. If the second graph shown is the one with the line through (0,0), then that's the correct graph. Since the user's image has two graphs, and the second (lower) one passes through the origin, the answer is the lower graph (or the second graph in the display).)