Which expression describes direct proportionality between y and x?

Which expression describes direct proportionality between y and x?

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

Answer: (A)

Direct proportionality means y grows in exact proportion to x: the ratio y/x stays the same for any x (excluding x = 0). The expression y = kx shows that relationship clearly, with k as the constant of proportionality. If x doubles, y doubles; if x is multiplied by any factor, y is multiplied by the same factor. Graphically, this is a straight line through the origin with slope k. The other forms don’t keep a constant y/x: y = k/x represents inverse proportionality; y = x + k adds a fixed amount to x, so the ratio isn’t constant; y = x^2 + k is a nonlinear, shifted curve. So y = kx is the expression that describes direct proportionality.

Direct proportionality means y grows in exact proportion to x: the ratio y/x stays the same for any x (excluding x = 0). The expression y = kx shows that relationship clearly, with k as the constant of proportionality. If x doubles, y doubles; if x is multiplied by any factor, y is multiplied by the same factor. Graphically, this is a straight line through the origin with slope k. The other forms don’t keep a constant y/x: y = k/x represents inverse proportionality; y = x + k adds a fixed amount to x, so the ratio isn’t constant; y = x^2 + k is a nonlinear, shifted curve. So y = kx is the expression that describes direct proportionality.