Slope and Rate of Change Practice

Front

What is the definition of slope?

Back

Slope is a measure of the steepness of a line, calculated as the ratio of the rise (vertical change) to the run (horizontal change) between two points on the line.

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

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

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, meaning the line falls from left to right.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

If a line has a slope of 1/2, what does this mean in terms of rise and run?

Back

For every 2 units of run (horizontal change), the line rises 1 unit (vertical change).

Front

What is the rate of change in a real-world context?

Back

The rate of change describes how one quantity changes in relation to another quantity, often expressed as a ratio.

Front

How can you interpret the slope in a graph representing distance over time?

Back

The slope represents the speed or rate of travel; a steeper slope indicates a faster speed.

Front

What is the formula for calculating the rate of change?

Back

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