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 form a straight line when graphed. Its rate of change is not constant, and it can take various forms such as quadratic, exponential, or logarithmic.

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 line represent?

Back

The slope of a line 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 of a linear function?

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

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-values and y-values in a table.

Front

What is the difference between a linear and a non-linear graph?

Back

A linear graph is a straight line, while a non-linear graph can be curved or have varying slopes.

Front

What is an example of a linear function?

Back

An example of a linear function is f(x) = 2x + 3.

Front

What is an example of a non-linear function?

Back

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

Front

How do you determine if an equation is linear or non-linear?

Back

An equation is linear if it can be rearranged into the form y = mx + b. If it contains variables raised to a power greater than one, it is non-linear.