which graph represents a proportional relationship?

Explanation:

Step1: Recall proportional - relationship property

A proportional relationship is of the form $y = kx$ where $k$ is a non - zero constant. Its graph is a straight line passing through the origin $(0,0)$.

Step2: Analyze each graph

• Graph A is a parabola ($y = ax^{2}$ form), not a straight - line, so it is not a proportional relationship.
• Graph B is a straight line and passes through the origin $(0,0)$. It can be represented by $y = kx$ for some non - zero $k$, so it represents a proportional relationship.
• Graph C is a hyperbola ($y=\frac{k}{x}$ form), not a straight line, so it is not a proportional relationship.
• Graph D is a cubic - like curve ($y = ax^{3}+bx^{2}+cx + d$ form), not a straight line, so it is not a proportional relationship.

Answer:

B