Calculating 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 (rise) to the horizontal change (run) between two points on the line.

Front

What is the slope formula?

Back

The slope (m) of a line is calculated using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

How do you find the slope of a line given two points (3, 4) and (6, 10)?

Back

Using the slope formula: m = (10 - 4) / (6 - 3) = 6 / 3 = 2.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no vertical change regardless of the horizontal change.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as it involves division by zero (no horizontal change).

Front

If a line has a slope of -1, what does this indicate about its direction?

Back

A slope of -1 indicates that the line descends from left to right, forming a 45-degree angle with the horizontal.

Front

Calculate the slope of the line passing through the points (2, 3) and (5, 7).

Back

Using the slope formula: m = (7 - 3) / (5 - 2) = 4 / 3.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that the line falls from left to right.

Front

If the slope of a line is 0, what can be said about the line?

Back

If the slope is 0, the line is horizontal and does not rise or fall.