Slope

Front

What is the definition of slope in mathematics?

Back

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

Front

How is slope calculated using two points (x1, y1) and (x2, y2)?

Back

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

Front

What does a positive slope indicate about a line on a graph?

Back

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

Front

What does a negative slope indicate about a line on a graph?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, 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, as there is no vertical change regardless of the horizontal change.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the horizontal change is 0, leading to division by zero.

Front

If a line has a slope of 3/2, what does this mean in terms of rise and run?

Back

A slope of 3/2 means that for every 2 units of horizontal change (run), the line rises 3 units (rise).

Front

How can slope be interpreted in real-world contexts, such as speed or rate of change?

Back

In real-world contexts, slope can represent rates of change, such as speed (distance over time) or growth rates (change in quantity over time).

Front

What is the slope of a line that falls at a rate of 2 cm per hour?

Back

The slope of the line is -2 cm/hour, indicating a decrease in height over time.

Front

How do you determine the slope from a graph?

Back

To determine the slope from a graph, select two points on the line, calculate the rise (vertical change) and run (horizontal change), and then use the slope formula: m = rise/run.