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 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.

Front

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

Back

To find the x-intercept, set f(x) = 0 and solve for x. The x-intercept is the point where the graph crosses the x-axis.

Front

What are opposite reciprocals?

Back

Opposite reciprocals are two numbers whose product is -1. For example, if the slope of one line is m, the slope of a line perpendicular to it is -1/m.

Front

What is the y-intercept of 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 equation f(x) = mx + b.

Front

What does a slope of zero indicate about a line?

Back

A slope of zero indicates that the line is horizontal, meaning there is no change in the y-value as the x-value changes.

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical, meaning the x-value does not change as the y-value changes.

Front

How do you evaluate a linear function at a specific point?

Back

To evaluate a linear function at a specific point, substitute the x-value into the function and solve for f(x).

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.

Front

What is the difference between increasing and decreasing functions?

Back

An increasing function has a positive slope, meaning as x increases, f(x) also increases. A decreasing function has a negative slope, meaning as x increases, f(x) decreases.