Identifying Linear Functions

Front

What is a linear function?

Back

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.

Front

What is the general form of a linear equation?

Back

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

Front

How can you identify a linear function from a table of values?

Back

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.

Front

What does the slope of a linear function represent?

Back

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

Front

What is the y-intercept in a linear function?

Back

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.

Front

Can a linear function have a variable multiplied by another variable?

Back

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

Front

What is the difference between linear and non-linear functions?

Back

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

Front

What is an example of a non-linear function?

Back

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

Front

How can you tell if a graph represents a linear function?

Back

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

Front

What is the significance of the slope being zero in a linear function?

Back

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