8.4B & 8.4C Rate of Change & Slope/ Rate of Change

Front

What is the definition of '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 or a slope.

Front

What does 'slope' represent in a graph?

Back

The slope represents the steepness of a line on a graph, indicating the rate of change between the x and y values.

Front

How do you calculate the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities when they are combined together, expressed as a quantity per one unit of another quantity.

Front

If a graph shows that 10 tickets cost $20, what is the unit cost per ticket?

Back

The unit cost per ticket is $2, calculated as $20 / 10 tickets.

Front

In the context of a graph, what does a positive slope indicate?

Back

A positive slope indicates that as one variable increases, the other variable also increases.

Front

What does a negative slope indicate in a graph?

Back

A negative slope indicates that as one variable increases, the other variable decreases.

Front

Back

This means that for every 3 units increase in the x-direction, the y-value decreases by 1 unit.

Front

How can you find the unit rate from a graph?

Back

To find the unit rate from a graph, identify the change in the dependent variable (y) for a change of 1 in the independent variable (x).

Front

What is the unit rate if 12 pages are read in 4 minutes?

Back

The unit rate is 3 pages per minute, calculated as 12 pages / 4 minutes.