Key Features of 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 f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does the y-intercept represent in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis. It is represented as (0, b) in the function f(x) = mx + b.

Front

How do you find the y-intercept using the cover-up method?

Back

To find the y-intercept using the cover-up method, set x = 0 in the equation and solve for y.

Front

What is the x-intercept of a linear function?

Back

The x-intercept is the point where the graph of the function crosses the x-axis. It is represented as (a, 0) in the function.

Front

How do you find the x-intercept of a linear equation?

Back

To find the x-intercept, set y = 0 in the equation and solve for x.

Front

What is the slope of a linear function?

Back

The slope (m) of a linear function represents the rate of change of y with respect to x. It is calculated as the change in y divided by the change in x.

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant of the line.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the line.

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 integers, and A should be non-negative.

Front

How can you identify the y-intercept from a graph?

Back

The y-intercept can be identified as the point where the graph intersects the y-axis, represented as (0, y).