Which of the following represents a linear relationship?

A linear relationship is defined as a relationship that can be graphically represented as a straight line when plotted on a coordinate system. In the context of equations, a linear equation is generally expressed in the form (y = mx + b), where (m) is the slope of the line, and (b) is the y-intercept. This form indicates that for every unit increase in (x), (y) changes by a constant amount (m).

The choice representing the linear relationship is characterized by a constant rate of change between (x) and (y). The presence of the variables in a linear manner (the exponent of (x) being 1) is vital. Therefore, the equation (y = mx + b) distinctly showcases this property, confirming it as the equation of a line.

The other choices involve non-linear relationships. For instance, (y = x^2) represents a quadratic relationship, producing a parabolic graph rather than a straight line, while (y = c + b^x) involves an exponential function, which is also non-linear. Meanwhile, (y = log(x)) describes a logarithmic function, another form that does not graph as