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 does an undefined slope represent?

Back

An undefined slope occurs in vertical lines where the change in x is zero, leading to division by zero, indicating that the line does not have a defined slope.

Front

What does a zero slope indicate about a line?

Back

A zero slope indicates that the line is horizontal, meaning there is no change in y as x changes.

Front

How can you determine the slope of a line given 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 you move horizontally (run), the line rises 3 units vertically (rise).

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.