Fill in the blank(s) to correctly complete each sentence. The equation y = 4x - 6 defines a function with independent variable______ and dependent variable ________ .

Key Concepts

Independent Variable

The independent variable is the input of a function, often represented by 'x' in equations. It is the variable that is manipulated or changed to observe its effect on the dependent variable. In the equation y = 4x - 6, 'x' is the independent variable, as its values determine the corresponding outputs of the function.

Dependent Variable

The dependent variable is the output of a function, typically represented by 'y'. It depends on the value of the independent variable, meaning its value changes in response to the independent variable's changes. In the equation y = 4x - 6, 'y' is the dependent variable, as it is calculated based on the value of 'x'.

Function Definition

A function is a relation that assigns exactly one output for each input from its domain. In mathematical terms, a function can be expressed as an equation, where the independent variable is used to compute the dependent variable. The equation y = 4x - 6 is a linear function, illustrating how changes in 'x' directly affect 'y'.