What is the standard form of a linear function?

The standard form of a linear function is characterized by the equation ( y = mx + b ), where ( m ) represents the slope of the line, and ( b ) is the y-intercept, which indicates the point where the line crosses the y-axis. This form directly expresses the relationship between the dependent variable ( y ) and the independent variable ( x ) in a linear manner, meaning that the graph of the equation will produce a straight line.

In this context, the slope ( m ) gives important information about the rate of change of the function, while the y-intercept ( b ) provides a starting value for ( y ) when ( x = 0 ). This foundational concept is essential in algebra and calculus for understanding linear relationships in various applications.

The other choices represent different types of functions. The first choice involves a quadratic function due to the ( x^2 ) term, which results in a parabolic graph rather than a straight line. The third choice represents an exponential function indicated by ( e^x ), which creates a curve that increases rapidly and is not linear at all. Lastly, the fourth choice shows a cubic function, as denoted by the ( x^3 \