Which statement accurately describes a linear function?

Which statement accurately describes a linear function?

• A. Its graph is a curved line
• B. It is a function with a changing rate of change
• C. Its graph is a line and the rate of change is constant
• D. It has no domain

Answer: (C)

A linear function has a constant rate of change and its graph is a straight line. This means that for equal steps in x, y changes by the same amount every time—the slope stays the same no matter where you are on the graph. If the rate of change varied, the graph would bend or curve, which isn’t a property of a linear function. Usually, a linear function can take any real number as x (its domain), unless a restriction is given, so it isn’t correct to say there’s no domain. For example, y = mx + b always forms a straight line because the slope m is constant.

A linear function has a constant rate of change and its graph is a straight line. This means that for equal steps in x, y changes by the same amount every time—the slope stays the same no matter where you are on the graph. If the rate of change varied, the graph would bend or curve, which isn’t a property of a linear function. Usually, a linear function can take any real number as x (its domain), unless a restriction is given, so it isn’t correct to say there’s no domain. For example, y = mx + b always forms a straight line because the slope m is constant.