Rate of Change from a Graph

Front

What is the rate of change?

Back

The rate of change is a measure of how much a quantity changes in relation to another quantity. It is often expressed as a ratio.

Front

Define constant of proportionality.

Back

The constant of proportionality is the constant value (k) that relates two proportional quantities, indicating how much one quantity changes in relation to another.

Front

What does a proportional graph look like?

Back

A proportional graph is a straight line that passes through the origin (0,0), indicating a constant rate of change.

Front

How do you find the rate of change from a graph?

Back

To find the rate of change, select two points on the graph, calculate the change in the y-values (rise) and the change in the x-values (run), and then divide rise by run.

Front

What is the formula for rate of change?

Back

Rate of change = (Change in y) / (Change in x) or (y2 - y1) / (x2 - x1).

Front

If k = 6 cookies/package, what does this mean?

Back

It means that for every package, there are 6 cookies.

Front

What does it mean if a graph is not proportional?

Back

If a graph is not proportional, it does not represent a constant rate of change and does not pass through the origin.

Front

If the constant of proportionality is k = 45, what does it indicate?

Back

It indicates that for every 1 hour, the boat travels 45 miles.

Front

What is an example of a rate of change in real life?

Back

An example is a car traveling at a speed of 60 miles per hour, meaning it covers 60 miles in one hour.

Front

How can you determine if a relationship is proportional?

Back

A relationship is proportional if the ratio of the two quantities remains constant and the graph is a straight line through the origin.