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 y-intercept of a function?

Back

The y-intercept is the point where the graph of a function crosses the y-axis. It occurs when x = 0.

Front

What is the x-intercept of a function?

Back

The x-intercept is the point where the graph of a function crosses the x-axis. It occurs when y = 0.

Front

True or False: The y-intercept of a function ALWAYS occurs where y is equal to zero.

Back

False. The y-intercept occurs where x is equal to zero.

Front

How can you determine if a function is linear or nonlinear?

Back

A function is linear if it can be expressed in the form y = mx + b. If it cannot, it is nonlinear.

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 standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are constants.

Front

Identify the x-intercept of the equation 2x + 3y = 6.

Back

The x-intercept is 3, found by setting y = 0 and solving for x.

Front

Identify the y-intercept of the equation 2x + 3y = 6.

Back

The y-intercept is 2, found by setting x = 0 and solving for y.

Front

What is the graphical representation of a linear function?

Back

The graphical representation of a linear function is a straight line.