Linear vs Non-linear

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in 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 graph to a straight line. Its graph can be a curve or any shape that is not straight.

Front

How can you identify a linear graph?

Back

A linear graph has a constant rate of change and forms a straight line when plotted on a coordinate plane.

Front

How can you identify a non-linear graph?

Back

A non-linear graph shows a variable rate of change and curves or bends when plotted on a coordinate plane.

Front

What does the slope of a linear function represent?

Back

The slope represents the rate of change of the function, indicating how much y changes for a unit change in x.

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

What is an example of a linear relationship in real life?

Back

An example of a linear relationship is the cost of items where each item has a fixed price, such as $5 per item.

Front

What is an example of a non-linear relationship in real life?

Back

An example of a non-linear relationship is the area of a circle as the radius increases, which grows quadratically.

Front

What does it mean for a graph to be a function?

Back

A graph is a function if every input (x-value) has exactly one output (y-value). This means no vertical line can intersect the graph at more than one point.

Front

What is the difference between a function and not a function?

Back

A function has one output for each input, while a relation that is not a function has at least one input with multiple outputs.