For a function to be considered linear, what characteristic must it have?

For a function to be characterized as linear, it must exhibit a constant slope throughout its domain. This means that the rate of change of the function remains the same, regardless of the values being considered. In mathematical terms, a linear function can be expressed in the form of ( y = mx + b ), where ( m ) represents the slope and ( b ) is the y-intercept. The constant slope indicates that for any equal change in the x-values, the change in the y-values will also be equal, resulting in a straight line when graphed.

This characteristic is essential because it defines the linearity of the function. Unlike nonlinear functions, which can curve or change direction, a linear function maintains its straight path. The other options reflect characteristics that do not universally define linear functions: changing direction may imply nonlinear behavior, while intersecting the x-axis is not a requirement for linearity, and falling to the left describes the direction of the slope but does not guarantee consistency or constancy in the slope across all points of the function.