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 graph?

Back

A linear graph can be identified by its straight line, constant slope, and the fact that it passes the vertical line test.

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?

Back

The y-intercept is the point where the graph of a function crosses the y-axis, represented by the value of y when x = 0.

Front

What is the difference between increasing and decreasing functions?

Back

An increasing function has a positive slope, meaning as x increases, y also increases. A decreasing function has a negative slope, meaning as x increases, y decreases.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, it is not a function.

Front

What is an example of a linear equation?

Back

An example of a linear equation is y = 3x + 2.

Front

What is an example of a nonlinear equation?

Back

An example of a nonlinear equation is y = x^2 + 1.

Front

How do you determine if a table of values represents a linear function?

Back

To determine if a table of values represents a linear function, check if the differences between consecutive y-values are constant for equal intervals of x.