Algebra 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 slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function. It indicates how much the y-value changes for a one-unit increase in the x-value.

Front

What is the y-intercept in a linear function?

Back

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

Front

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

Back

The slope (m) can be 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 is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value).

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as the x-values increase, the y-values also increase. This is indicated by a positive slope.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as the x-values increase, the y-values decrease. This is indicated by a negative slope.

Front

What is a horizontal line in terms of a linear function?

Back

A horizontal line is a linear function with a slope of 0, represented by the equation y = b, where b is a constant.

Front

What is a vertical line in terms of a linear function?

Back

A vertical line is not a function because it does not pass the vertical line test; it has an undefined slope.