Slope

Front

What is the definition of slope?

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

How is slope calculated?

Back

Slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What does a positive slope indicate?

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?

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, 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

What does a slope of 1 represent?

Back

A slope of 1 represents a line that rises one unit vertically for every one unit it moves horizontally, creating a 45-degree angle with the x-axis.

Front

What is the relationship between slope and steepness?

Back

The steeper the line, the greater the absolute value of the slope. A slope of 2 is steeper than a slope of 1.

Front

What are the four types of slope?

Back

The four types of slope are positive slope, negative slope, zero slope, and undefined slope.

Front

How does slope relate to real-world situations?

Back

Slope can represent rates of change in real-world contexts, such as speed (distance over time) or cost (price over quantity).