Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, which can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line, meaning the rate of change between x and y is not constant.

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant rate of change between the x-coordinates and y-coordinates.

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x, calculated as 'rise over run'.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

How do you find the slope from 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 equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean if a function has an undefined slope?

Back

An undefined slope indicates a vertical line, where the change in x is zero, making the slope calculation impossible.

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent rates such as speed, cost per item, or any other ratio of change between two quantities.

Front

How can you determine if a graph represents a linear function?

Back

A graph represents a linear function if it forms a straight line without any curves or bends.