Slope from Two Points

Front

What is the definition of slope in mathematics?

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 between two points (x1, y1) and (x2, y2)?

Back

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

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical, meaning it goes straight up and down, and there is no horizontal change.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating that there is no vertical change as you move along the line.

Front

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

Back

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

Front

Find the slope of the line that passes through the points (1, 2) and (4, 8).

Back

The slope is m = (8 - 2) / (4 - 1) = 6 / 3 = 2.

Front

What is the slope of the line through the points (-14, -5) and (-8, 2)?

Back

The slope is m = (2 - (-5)) / (-8 - (-14)) = 7 / 6.

Front

If the slope of a line is 1/2, what does this mean?

Back

A slope of 1/2 means that for every 2 units you move horizontally to the right, you move 1 unit up vertically.

Front

What is the slope of the line that passes through the points (3, 4) and (3, 7)?

Back

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

Front

Find the slope of the line that passes through the points (0, 0) and (5, 10).

Back

The slope is m = (10 - 0) / (5 - 0) = 10 / 5 = 2.