Which phrase best describes the graph of a proportional relationship?

• A. A curved line that starts at the origin
• B. A straight line that passes through the origin
• C. A horizontal line
• D. A straight line that does not pass through the origin

Answer: (B)

Verified step by step guidance

1. Understand that a proportional relationship between two variables means one variable is a constant multiple of the other. Mathematically, this can be expressed as \(y = kx\), where \(k\) is a constant.
2. Recognize that the graph of \(y = kx\) is a straight line because the relationship between \(x\) and \(y\) is linear.
3. Note that since \(y = kx\) has no constant term added or subtracted, the line must pass through the origin \((0,0)\), because when \(x=0\), \(y=0\).
4. Eliminate options that describe a curve or a line that does not pass through the origin, as these do not fit the definition of proportionality.
5. Conclude that the phrase 'A straight line that passes through the origin' best describes the graph of a proportional relationship.