Slope Rise Over Run and Slope Formula

Front

What is the definition of slope in mathematics?

Back

The slope of a line is a measure of its steepness, typically represented as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

How do you calculate the slope using rise over run?

Back

To calculate the slope using rise over run, divide the vertical change (rise) by the horizontal change (run) between two points on the line: Slope (m) = Rise/Run.

Front

What is the slope formula?

Back

The slope formula is given by m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

Find the slope of the line given the points (2, 3) and (5, 7).

Back

The slope is m = (7 - 3) / (5 - 2) = 4/3.

Front

Find the slope of the line given the points (1, 2) and (4, 5).

Back

The slope is m = (5 - 2) / (4 - 1) = 3/3 = 1.

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 is the slope of a horizontal line?

Back

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

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the horizontal change (run) is 0, leading to division by zero.

Front

Find the slope of the line given the points (2, -7) and (-1, 6).

Back

The slope is m = (6 - (-7)) / (-1 - 2) = 13 / -3 = -13/3.