Linear vs Non Linear Equations

Front

What is a linear equation?

Back

An equation that makes a straight line when graphed, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear equation?

Back

An equation that does not form a straight line when graphed, which can include curves, circles, and other shapes.

Front

What is the slope of a linear function?

Back

The slope (m) 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?

Back

The point where the graph of a function intersects the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if each output value is paired with exactly one input value, meaning no two different inputs produce the same output.

Front

What is the domain of a function?

Back

The set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The set of all possible output values (y-values) that a function can produce.

Front

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

Back

If the differences between consecutive y-values are constant for equal intervals of x, the function is linear.

Front

What is a function?

Back

A relation where each input (x) has exactly one output (y).

Front

What is the difference between a function and a relation?

Back

A relation can have multiple outputs for a single input, while a function must have only one output for each input.