Linear Functions

A linear function is a function that graphs to a straight line. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

The slope (m) represents the rate of change of the function. It indicates how much y changes for a unit change in x.

The y-intercept (b) is the point where the line crosses the y-axis. It represents the value of y when x is 0.

A relation is a function if each input (x-value) has exactly one output (y-value). If any x-value is repeated with different y-values, it is not a function.

A function has a unique output for every input, while a non-function has at least one input that corresponds to multiple outputs.

A table represents a linear function if the differences between consecutive y-values are constant when the x-values increase by the same amount.

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

A vertical line has an undefined slope and is not a function because it has multiple y-values for the same x-value.

A horizontal line has a slope of 0 and is a function because it has one y-value for every x-value.