Linear Or Not Linear (graphs and tables)

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 various shapes, and it does not have a constant rate of change.

Front

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

Back

A linear function will have a constant difference in the y-values for equal intervals in the x-values.

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

Front

Can a linear function have a negative slope?

Back

Yes, a linear function can have a negative slope, which means that as the x-values increase, the y-values decrease.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.

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 do you determine if a graph is linear or nonlinear?

Back

A graph is linear if it forms a straight line. If the graph curves or changes direction, it is nonlinear.

Front

What is the difference between a linear equation and a nonlinear equation?

Back

A linear equation represents a straight line, while a nonlinear equation represents a curve or a more complex shape.