Slope Basics Flashcard

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, resulting in an upward trend.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, resulting in a downward trend.

Front

What does a zero slope indicate?

Back

A zero slope indicates a horizontal line where there is no change in the y-value as the x-value changes.

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line where the x-value remains constant while the y-value changes.

Front

If a line passes through the points (2, 3) and (4, 7), what is the slope?

Back

The slope is 2, calculated as (7 - 3) / (4 - 2).

Front

If a line has a slope of 4, what does this mean in terms of rise over run?

Back

A slope of 4 means that for every 1 unit you move horizontally (run), the line rises 4 units (rise).

Front

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

Back

The slope of a perfectly horizontal line is 0.

Front

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

Back

The slope of a perfectly vertical line is undefined.