Linear Functions

Front

What is the definition of a function?

Back

Every input has only ONE output.

Front

What is a linear function?

Back

A function that can be graphically represented as a straight line.

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 differences in x-values.

Front

What is the slope of a linear function?

Back

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

Front

What is the y-intercept of a linear function?

Back

The value of y when x is 0, represented as the point (0, b) in the equation y = mx + b.

Front

What does the equation y = mx + b represent?

Back

The slope-intercept form of a linear equation, where m is the slope and b is the y-intercept.

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions have a constant rate of change, while nonlinear functions do not.

Front

What is an example of a linear function?

Back

y = 2x + 1.

Front

What is an example of a nonlinear function?

Back

y = x^2.