Which of the following graphs best represents a proportional relationship between two variables?

• A. A straight line with a positive y-intercept
• B. A straight line passing through the origin
• C. A horizontal line
• D. A curve that increases at a decreasing rate

Answer: (B)

Verified step by step guidance

1. Understand what a proportional relationship means: it implies that one variable is directly proportional to another, which can be expressed as \(y = kx\), where \(k\) is a constant of proportionality.
2. Recall that in a proportional relationship, when \(x = 0\), \(y\) must also be \$0\(, so the graph must pass through the origin \)(0,0)$.
3. Analyze the options: a straight line with a positive y-intercept does not pass through the origin, so it cannot represent a proportional relationship.
4. A horizontal line means \(y\) is constant regardless of \(x\), which is not proportional because \(y\) does not change with \(x\).
5. A curve that increases at a decreasing rate is nonlinear and does not represent a constant ratio between \(y\) and \(x\), so it is not proportional.