Which expression represents a linear relationship between two variables y and x?

Which expression represents a linear relationship between two variables y and x?

• A. y=b+mx
• B. y=mx^2 + b
• C. y=e^x
• D. y=log x

Answer: (A)

A linear relationship means y changes at a constant rate as x changes, which plots as a straight line. The form that expresses this directly is y = m x + b (or y = b + m x), where m is the slope (how much y changes per unit of x) and b is the y-intercept (the value of y when x is zero). The given expression matches this linear form, showing x is only to the first power and added to a constant after being scaled by m. The other expressions involve x squared, an exponential function, or a logarithmic function, which produce curved graphs and are not linear.

A linear relationship means y changes at a constant rate as x changes, which plots as a straight line. The form that expresses this directly is y = m x + b (or y = b + m x), where m is the slope (how much y changes per unit of x) and b is the y-intercept (the value of y when x is zero). The given expression matches this linear form, showing x is only to the first power and added to a constant after being scaled by m. The other expressions involve x squared, an exponential function, or a logarithmic function, which produce curved graphs and are not linear.