Identifying 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 the general form of a linear function?

Back

The general form of a linear function is y = mx + b, where m represents the slope and b represents the y-intercept.

Front

Which of the following is NOT a linear function? y = 3x, y = x², y = 5x - 9, y = 3(x + 4)

Back

y = x² is NOT a linear function.

Front

How can you determine if a relation is a function?

Back

A relation is a function if each input (x-value) is associated with exactly one output (y-value).

Front

Is the function y = 2x + 3 linear or nonlinear?

Back

Linear Function.

Front

Is the function y = x² + 4 linear or nonlinear?

Back

Nonlinear Function.

Front

What does the slope of a linear function represent?

Back

The slope 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 in 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

Given the points (1, 2) and (3, 6), is the relation linear?

Back

Yes, the relation is linear because the slope between the points is constant.

Front

What is the difference between a linear function and a nonlinear function?

Back

A linear function has a constant rate of change and graphs as a straight line, while a nonlinear function does not have a constant rate of change and can graph as a curve.