If there is a linear relationship between y and x, which expression represents this relationship?

If there is a linear relationship between y and x, which expression represents this relationship?

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

Answer: (A)

A linear relationship between y and x means y changes at a constant rate as x changes, which is described by the slope-intercept form y = mx + b. Here, m is the slope (rate of change) and b is the y-intercept (the value of y when x is zero). The expression y = b + mx is just another way to write the same relationship with the terms in a different order; it captures any possible slope and intercept, so it represents the general linear relationship. The other forms don’t fit as well: y = mx^2 + b contains x squared, which makes the relation nonlinear (it would be a curve). y = log x is a logarithmic relationship, not linear. y = x + b is linear too, but it fixes the slope at 1, so it doesn’t cover all possible linear relationships where the slope could be anything.

A linear relationship between y and x means y changes at a constant rate as x changes, which is described by the slope-intercept form y = mx + b. Here, m is the slope (rate of change) and b is the y-intercept (the value of y when x is zero). The expression y = b + mx is just another way to write the same relationship with the terms in a different order; it captures any possible slope and intercept, so it represents the general linear relationship.

The other forms don’t fit as well: y = mx^2 + b contains x squared, which makes the relation nonlinear (it would be a curve). y = log x is a logarithmic relationship, not linear. y = x + b is linear too, but it fixes the slope at 1, so it doesn’t cover all possible linear relationships where the slope could be anything.