Slope from Two Points

Front

What is the definition of slope in mathematics?

Back

The slope is a measure of the steepness or incline of a line, defined 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 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 is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x (run) is zero, leading to division by zero in the slope formula.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0 because there is no vertical change (rise) as the x-coordinate changes.

Front

Given the points (2, 3) and (5, 11), what is the slope?

Back

Using the formula m = (y2 - y1) / (x2 - x1), the slope is m = (11 - 3) / (5 - 2) = 8 / 3.

Front

If the slope of a line is 4, what does this mean in terms of rise and run?

Back

A slope of 4 means that for every 1 unit of horizontal change (run), the vertical change (rise) is 4 units.

Front

What is 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 / 4 = 1.

Front

How can you determine if two lines are parallel using their slopes?

Back

Two lines are parallel if they have the same slope.