Types of 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 to the horizontal change between two points on the line.

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 zero, indicating no vertical change as the x-value changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as there is no horizontal change.

Front

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

Back

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

Front

What is the significance of a slope of zero in real-world applications?

Back

A slope of zero can represent a constant value, such as a flat road or a stable temperature over time.

Front

In what scenarios would you encounter an undefined slope?

Back

An undefined slope occurs in scenarios involving vertical lines, such as a wall or a cliff.

Front

What is the relationship between slope and rate of change?

Back

Slope represents the rate of change between two variables; a steeper slope indicates a greater rate of change.

Front

How can slope be used to determine the direction of a trend in data?

Back

A positive slope indicates an upward trend, while a negative slope indicates a downward trend in the data.