Question

which of the following graphs represents a proportional relationship? a. x b. z c. y d. w

Explanation:

A proportional relationship is represented by a straight line that passes through the origin \((0,0)\) (since the equation is \(y = kx\), where \(k\) is the constant of proportionality, so when \(x = 0\), \(y = 0\)) and has a constant slope. Let's analyze each graph:

• Graph W: The line does not pass through the origin (it has a y - intercept other than 0), so it is not proportional.
• Graph X: The line is straight and passes through the origin \((0,0)\). It has a constant slope, so it represents a proportional relationship.
• Graph Y: It is a piece - wise function with a peak, not a straight line with a constant slope throughout, and does not represent a proportional relationship.
• Graph Z: The line does not pass through the origin (it has a y - intercept other than 0), so it is not proportional.

Answer:

A. X