Question

which graph represents a function with direct variation?

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 that passes through the origin \((0,0)\) (since when \( x = 0 \), \( y = 0 \)).

Step2: Analyze Each Graph

• First graph: The line does not pass through the origin (it has a \( y \)-intercept of 3), so it's not direct variation.
• Second graph: The line does not pass through the origin (it has a negative \( y \)-intercept), so it's not direct variation.
• Third graph: The line passes through the origin \((0,0)\), so it could represent a direct variation function (\( y = kx \) with some \( k \)).
• Fourth graph: The line does not pass through the origin (it has a \( y \)-intercept that's not 0), so it's not direct variation.

Answer:

The third graph (the one with the orange line passing through the origin) represents a function with direct variation.