A graph is a straight line through the point (0, 5). Can the graph represent a proportional relationship? Explain.

Question

Yes; the constant of proportionality is 5.



Yes; the equation of the line can be written in the form y = kx, where k = 5.



Yes; the graph is a straight line that crosses the y-axis at (0, 5).



No; the graph of a proportional relationship must pass through (0, 0).

Answer 1

No; the graph of a proportional relationship must pass through (0, 0).

A proportional relationship is defined as one in which the ratio of the two quantities remains constant, and it is typically represented by a line that passes through the origin (0, 0). In this case, the graph passes through (0, 5), not (0, 0), indicating that while there may be a consistent relationship, it is not proportional since a proportional relationship cannot have a y-intercept other than zero. Thus, the correct answer is that it cannot represent a proportional relationship.