Identify Slope Types

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 is the formula for calculating slope?

Back

The formula for calculating slope (m) is m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are 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, resulting in an upward trend.

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, resulting in a downward trend.

Front

What is an undefined slope?

Back

An undefined slope occurs in vertical lines where the change in x is zero, making the slope calculation (y2 - y1) / (0) impossible.

Front

What is a zero slope?

Back

A zero slope occurs in horizontal lines where the change in y is zero, indicating that the line is flat and does not rise or fall.

Front

How can you visually identify a positive slope on a graph?

Back

A positive slope can be visually identified on a graph as a line that rises from left to right.

Front

How can you visually identify a negative slope on a graph?

Back

A negative slope can be visually identified on a graph as a line that falls from left to right.

Front

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

Back

Slope is significant in real-world applications such as determining the rate of change in economics, physics, and engineering, as well as in analyzing trends in data.

Front

What is the relationship between slope and linear equations?

Back

In linear equations of the form y = mx + b, 'm' represents the slope of the line, indicating its steepness and direction.