SLOPE AS RATE OF CHANGE

Front

What is the definition of slope in the context of rate of change?

Back

Slope is a measure of the steepness or incline of a line, representing the rate of change of one variable with respect to another.

Front

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

Back

Average rate of change = (Change in y) / (Change in x).

Front

If a climber's altitude changes from 400 feet to 700 feet over 4 hours, what is the average rate of change?

Back

Average rate of change = (700 - 400) / (6 - 2) = 75 feet per hour.

Front

What does a slope of 0 indicate about a graph?

Back

A slope of 0 indicates that there is no change in the y-value as the x-value changes; the line is horizontal.

Front

What does a negative slope indicate about the relationship between two variables?

Back

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

Front

What is the formula for finding the slope between two points (x1, y1) and (x2, y2)?

Back

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

Front

What is the significance of a constant rate of change in a graph?

Back

A constant rate of change means that the slope of the line is the same throughout, indicating a linear relationship.

Front

If Mrs. Taylor is 10 feet off the ground at 0 seconds and 20 feet at 5 seconds, what is her rate of change?

Back

Rate of change = (20 - 10) / (5 - 0) = 2 feet per second.

Front

What does it mean if a graph has a slope of 5 miles per week?

Back

It means that for every week that passes, the distance increases by 5 miles.

Front

How can you determine if a graph represents a constant rate of change?

Back

If the graph is a straight line, it represents a constant rate of change.