7-5-6 PLUS Slope and Rates of Change

Front

What is the definition of slope in mathematics?

Back

Slope is a measure of the steepness or incline of a line, calculated as the change in the vertical direction (rise) divided by the change in the horizontal direction (run).

Front

What does a constant rate of change mean?

Back

A constant rate of change means that the quantity changes at a steady rate over time, resulting in a straight line when graphed.

Front

How do you calculate the average rate of change?

Back

Average rate of change is calculated by taking the difference in the output values (y-values) divided by the difference in the input values (x-values) over a specific interval.

Front

What is the slope of a line that rises 3 units for every 4 units it runs?

Back

The slope is 3/4.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, meaning the line goes down from left to right.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

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

Back

The average rate of change is 75 feet per hour.

Front

What does a variable rate of change mean?

Back

A variable rate of change means that the quantity changes at different rates over time, resulting in a curve when graphed.

Front

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

Back

If the graph is a straight line, it represents a constant rate of change; if it is curved, it represents a variable rate of change.