Which equation represents a direct variation between y and x?

Which equation represents a direct variation between y and x?

• A. y = x + k
• B. y = kx
• C. y = x^2
• D. y = k/x

Answer: (B)

Direct variation means y is proportional to x, so there’s a constant k with y = kx. This captures the idea that when x changes, y changes by the same factor, and the ratio y/x remains constant at k. The form y = x + k would shift the line up or down and gives a nonzero intercept, so it doesn’t scale y with x. The form y = x^2 is quadratic, not proportional, since y grows with the square of x. The form y = k/x represents inverse variation, where y varies inversely with x, not directly. Therefore, the equation that represents a direct variation between y and x is y = kx.

Direct variation means y is proportional to x, so there’s a constant k with y = kx. This captures the idea that when x changes, y changes by the same factor, and the ratio y/x remains constant at k. The form y = x + k would shift the line up or down and gives a nonzero intercept, so it doesn’t scale y with x. The form y = x^2 is quadratic, not proportional, since y grows with the square of x. The form y = k/x represents inverse variation, where y varies inversely with x, not directly. Therefore, the equation that represents a direct variation between y and x is y = kx.