Linear vs 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 create a straight line when graphed. It can have curves, bends, or changes in direction.

Front

What is the slope in a linear function?

Back

The slope (m) in a linear function represents the rate of change of y with respect to x. It indicates how steep the line is.

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. It represents the value of y when x is 0.

Front

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

Back

A linear function will have a constant rate of change between the x and y values. If the differences in y-values divided by the differences in x-values are constant, the function is linear.

Front

What is the equation of a linear function?

Back

The general form of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

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

What does it mean for a function to have a constant rate of change?

Back

A constant rate of change means that for every unit increase in x, the change in y is always the same, indicating a straight line.

Front

How can you tell if a graph is linear or nonlinear?

Back

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

Front

What is the significance of the equation y = 8x?

Back

The equation y = 8x represents a linear function with a slope of 8 and a y-intercept of 0.