14. Average Rate of Change, Slope, and Y-intercept

Front

What is the average rate of change?

Back

The average rate of change of a function over an interval is the change in the function's value divided by the change in the input value over that interval.

Front

How do you calculate the slope of a line?

Back

The slope (m) is calculated as the change in y (rise) divided by the change in x (run) between two points on the line: m = (y2 - y1) / (x2 - x1).

Front

What does a slope of 0 indicate?

Back

A slope of 0 indicates that the line is horizontal, meaning there is no change in y as x changes.

Front

What does a positive slope indicate?

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship.

Front

What is the y-intercept of a line?

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

What is a linear function?

Back

A linear function is a function that graphs to a straight line and has a constant average rate of change.

Front

How can you determine if a function is linear from a table of values?

Back

A function is linear if the average rate of change (slope) between any two points is constant.

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 the term 'rise over run' refer to?

Back

'Rise over run' refers to the slope of a line, calculated as the vertical change (rise) divided by the horizontal change (run).