Key Features of Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane as a straight line. It has the form y = 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 the value of y when x = 0.

Front

How do you find the y-intercept from the equation 4x + 2y = -12?

Back

To find the y-intercept, set x = 0. The equation becomes 2y = -12, so y = -6. Thus, the y-intercept is (0, -6).

Front

What is the x-intercept in a linear function?

Back

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

Front

How do you find the x-intercept from the equation 4x + 2y = -12?

Back

To find the x-intercept, set y = 0. The equation becomes 4x = -12, so x = -3. Thus, the x-intercept is (-3, 0).

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 (rise/run).

Front

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

Back

The slope m is calculated using the formula m = (y2 - y1) / (x2 - x1).

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

What does it mean if a linear function has a positive slope?

Back

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

Front

What does it mean if a linear function has a negative slope?

Back

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