Understand 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 slope in a linear function?

Back

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

Front

What is the y-intercept in a linear function?

Back

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

Front

How can you identify a non-linear function?

Back

A non-linear function can be identified by the presence of exponents, variables multiplied together, or any other operation that does not result in a straight line when graphed.

Front

What does it mean for a function to be linear?

Back

A function is linear if it can be expressed in the form f(x) = mx + b, resulting in a straight line when graphed.

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

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

Back

Linear functions produce straight-line graphs and have a constant rate of change, while non-linear functions produce curves and have varying rates of change.

Front

What is an example of a linear function?

Back

An example of a linear function is f(x) = 2x + 3.

Front

What is an example of a non-linear function?

Back

An example of a non-linear function is f(x) = x^2.

Front

How do you determine if a graph represents a linear function?

Back

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