Linear vs Non-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 y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a non-linear function?

Back

A non-linear function is a function that does not create a straight line when graphed. It can include curves, parabolas, and other shapes.

Front

How can you identify a linear equation?

Back

A linear equation can be identified by its highest exponent being 1, meaning it does not have variables raised to a power greater than 1.

Front

What are the characteristics of a linear graph?

Back

A linear graph has a constant slope, meaning the rate of change is the same throughout the graph.

Front

What are the characteristics of a non-linear graph?

Back

A non-linear graph can have varying slopes, curves, and may change direction, indicating that the rate of change is not constant.

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, indicating how much y changes for a unit change in x.

Front

What does the y-intercept represent in a linear function?

Back

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

Front

Give an example of a linear function.

Back

An example of a linear function is y = 2x + 3.

Front

Give an example of a non-linear function.

Back

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

Front

What is the significance of exponents in identifying non-linear equations?

Back

Exponents greater than 1 in an equation indicate that it is non-linear, as they create curves rather than straight lines.