Reviewing Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, represented by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear function?

Back

The slope represents the rate of change of the function; it indicates how much y changes for a unit change in x.

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 y-intercept in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as x increases, y also increases, meaning the function is increasing.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as x increases, y decreases, meaning the function is decreasing.

Front

What does a slope of zero indicate?

Back

A slope of zero indicates a horizontal line, meaning there is no change in y as x changes.

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, meaning x does not change as y changes.

Front

What is the range of a linear function?

Back

The range of a linear function is the set of all possible output values (y-values) that the function can produce.

Front

How can you determine if a linear function is increasing or decreasing from its graph?

Back

If the line rises from left to right, the function is increasing; if it falls from left to right, the function is decreasing.