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

Step2: Analyze Each Graph

• First Graph: A parabola (quadratic function, \( y = ax^2 \)), not a straight line through origin. Eliminate.
• Second Graph: A straight line, but it does not pass through \((0,0)\) (y-intercept is 1). Eliminate.
• Third Graph: A V - shaped graph (absolute value function, \( y = |x| + c \)), y - intercept is 1 (not 0). Eliminate.
• Fourth Graph: A straight line passing through the origin \((0,0)\), which fits \( y = kx \) (direct variation) form.

Answer:

The graph in the bottom - right (the fourth graph) represents a function with direct variation.