Constant Rate of Change

Front

What is the definition of a constant rate of change?

Back

A constant rate of change refers to a situation where the change in one quantity is consistent with the change in another quantity over a specific interval.

Front

How is the gradient of a line related to the rate of change?

Back

The gradient (or slope) of a line represents the rate of change between two variables; a positive gradient indicates an increase, while a negative gradient indicates a decrease.

Front

What are the units typically used to describe a rate of change?

Back

Units of rate of change can vary, but they often include combinations of the quantities being measured, such as miles per hour, calories per minute, etc.

Front

What does the point (20, 5) represent in a real-world context?

Back

In this context, the point (20, 5) indicates that delivering 20 newspapers results in earning $5.

Front

How do you calculate the rate of change from two points on a graph?

Back

The rate of change can be calculated using the formula: (change in y) / (change in x) between the two points.

Front

What is the significance of a negative gradient in a graph?

Back

A negative gradient indicates that as one variable increases, the other variable decreases, showing an inverse relationship.

Front

What does a constant rate of change imply about the relationship between two variables?

Back

A constant rate of change implies a linear relationship between the two variables, meaning they change at a consistent rate.

Front

How can you identify a constant rate of change from a table of values?

Back

A constant rate of change can be identified if the differences between consecutive y-values divided by the differences between consecutive x-values are the same.

Front

What is the formula for calculating the slope of a line?

Back

The formula for calculating the slope (m) is: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What does the term 'rate' refer to in mathematics?

Back

In mathematics, 'rate' refers to a ratio that compares two different kinds of quantities, often expressed as a fraction.