Identifying Linear Functions

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

A linear function will have a constant rate of change, meaning the difference in y-values divided by the difference in x-values will be the same for all pairs of points.

The slope represents the rate of change of the function; it indicates how much y changes for a unit change in x.

The y-intercept is the point where the graph of the function crosses the y-axis, represented by the value of b in the equation f(x) = mx + b.

No, a linear function cannot have terms like xy; it can only have terms that are either constant or linear in one variable.

Linear functions produce straight-line graphs, while non-linear functions produce curves or other shapes.

An example of a non-linear function is f(x) = x^2, which produces a parabolic graph.

A graph represents a linear function if it forms a straight line without any curves.

If the slope is zero, the function is constant, meaning it does not change regardless of the value of x.