Slope from a Graph

Front

What is the definition of slope?

Back

The slope of a line is a measure of its steepness, usually represented as 'm' in the equation of a line (y = mx + b). It is calculated as the change in y (rise) divided by the change in x (run).

Front

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

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y 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 x increases, y decreases, meaning the line falls from left to right.

Front

What does a slope of zero mean?

Back

A slope of zero means the line is horizontal, indicating that there is no change in y as x changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs with a vertical line, where x remains constant and y changes, leading to division by zero.

Front

If a line rises 3 units for every 2 units it runs, what is the slope?

Back

Slope (m) = rise/run = 3/2.

Front

If a line falls 4 units for every 1 unit it runs, what is the slope?

Back

Slope (m) = rise/run = -4/1 = -4.

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.