Linear or NonLinear

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 nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed. Its equation may involve exponents, roots, or other operations that create curves.

Front

Identify the equation: y = 5x^3. Is it linear or nonlinear?

Back

Nonlinear

Front

Identify the equation: y = 3x + 5. Is it linear or nonlinear?

Back

Linear

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 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 equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

Can a linear function have a slope of zero?

Back

Yes, a linear function can have a slope of zero, which means it is a horizontal line.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2, which represents a parabola.

Front

How can you determine if an equation is linear or nonlinear?

Back

You can determine if an equation is linear or nonlinear by checking if it can be rearranged into the form y = mx + b or if it contains variables raised to powers other than one.