Rate of Change

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the slope, which represents the change in the y-value for a unit change in the x-value.

Front

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

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What does a slope of 0 indicate about a line?

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.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as x increases, y decreases.

Front

What is the rate of change of a function represented by a table of values?

Back

The rate of change can be calculated by finding the difference in y-values divided by the difference in x-values for any two points.

Front

What is the significance of a non-constant slope in a function?

Back

A non-constant slope indicates that the function is non-linear, meaning the rate of change varies.

Front

How can you interpret the rate of change in a real-world context?

Back

The rate of change can represent speed, cost per item, or any other quantity that changes with respect to another.

Front

What is the formula for the slope of a line given two points?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

If a line has a slope of 11/2, what does this mean?

Back

This means that for every 2 units increase in x, y increases by 11 units.