Linear Functions

Front

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

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the y-coordinate with respect to the x-coordinate. It indicates how steep the line is and the direction it goes (positive or negative).

Front

How do you calculate the slope between 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 slope of the line represented by the equation y = -5/4x + 3?

Back

The slope of the line is -5/4.

Front

What is the y-intercept in the equation y = 2x + 4?

Back

The y-intercept is 4, which is the point where the line crosses the y-axis.

Front

What does it mean if a line has a positive slope?

Back

A line with a positive slope rises from left to right, indicating that as x increases, y also increases.

Front

What does it mean if a line has a negative slope?

Back

A line with a negative slope falls from left to right, indicating that as x increases, y decreases.

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

How can you determine if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1.

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.