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 an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical, meaning it goes straight up and down, and there is no horizontal change.

Front

What does a positive slope indicate about the direction of a line?

Back

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

Front

What does a negative slope indicate about the direction of a line?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, resulting in a line that falls from left to right.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is zero, indicating that there is no vertical change as the x-values change.

Front

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

Back

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

Front

What is the slope of a line that is perfectly vertical?

Back

The slope of a perfectly vertical line is undefined.

Front

What is the slope of a line that is perfectly horizontal?

Back

The slope of a perfectly horizontal line is zero.

Front

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

Back

A slope of 3 means that for every 1 unit of horizontal change (run), the line rises 3 units (rise).

Front

What is the relationship between slope and the angle of inclination of a line?

Back

The slope of a line is related to the angle of inclination; a steeper line has a greater slope and a larger angle of inclination.