Linear or Non-Linear

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 graph can be curved or have varying slopes.

Front

How can you identify a linear function from its equation?

Back

If the equation can be expressed in the form y = mx + b, it is linear. For example, y = 2x + 3 is linear.

Front

What does the slope of a linear function represent?

Back

The slope (m) 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 (b) is the point where the graph of the function crosses the y-axis, represented as (0, b).

Front

Is the function y = 3x + 2 linear or nonlinear?

Back

Linear

Front

Is the function y = x^2 + 1 linear or nonlinear?

Back

Nonlinear

Front

What is the graphical representation of a linear function?

Back

A linear function is represented by a straight line on a graph.

Front

What is the difference between linear and nonlinear graphs?

Back

Linear graphs are straight lines, while nonlinear graphs can be curves or have varying slopes.

Front

Can a linear function have a negative slope?

Back

Yes, a linear function can have a negative slope, indicating that as x increases, y decreases.