Slope from Two Points

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented as 'm'. It is calculated 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 from two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-coordinate increases, the y-coordinate 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-coordinate increases, the y-coordinate 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 vertical change as the x-coordinate changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs when a line is vertical, meaning there is no horizontal change as the x-coordinate remains constant.

Front

Find the slope of the line that passes through the points (1, 2) and (3, 6).

Back

The slope is m = (6 - 2) / (3 - 1) = 4 / 2 = 2.

Front

Find the slope of the line that passes through the points (2, 3) and (2, 5).

Back

The slope is undefined because the x-coordinates are the same (2), indicating a vertical line.

Front

If the slope of a line is 3, what does this mean in terms of rise and run?

Back

For every 3 units the line rises vertically, it runs 1 unit horizontally to the right.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.