Average Rate of Change - Word Problems

Front

What is the average rate of change?

Back

The average rate of change is the change in the value of a quantity divided by the change in time or another variable. It represents how much one quantity changes on average with respect to another.

Front

How do you calculate the average rate of change between two points?

Back

To calculate the average rate of change between two points (x1, y1) and (x2, y2), use the formula: (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate in a graph?

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

What does a zero slope indicate in a graph?

Back

A zero slope indicates that there is no change in the value of the dependent variable as the independent variable changes; the line is horizontal.

Front

What does an undefined slope indicate in a graph?

Back

An undefined slope indicates a vertical line where the x-value does not change, leading to division by zero in the slope formula.

Front

If Justin can type 408 words in 4 minutes, what is his unit rate?

Back

The unit rate is 102 words per minute (408 words / 4 minutes).

Front

How can you find the number of words Justin can type in 7 minutes using the unit rate?

Back

Multiply the unit rate (102 words/minute) by 7 minutes to find that he can type 714 words in 7 minutes.

Front

What is the average rate of change for a climber who goes from 400 feet to 700 feet in 4 hours?

Back

The average rate of change is 75 feet per hour ((700 - 400) / (6 - 2)).

Front

How do you determine the average rate of change over different intervals?

Back

Calculate the average rate of change for each interval using the formula (y2 - y1) / (x2 - x1) and compare the results.