Calculating Slopes

Front

What is the definition of slope in mathematics?

Back

The 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) between two points (x1, y1) and (x2, y2) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

How do you calculate the slope of a line given two points?

Back

To calculate the slope, subtract the y-coordinate of the first point from the y-coordinate of the second point (rise), and subtract the x-coordinate of the first point from the x-coordinate of the second point (run), then divide the rise by the run.

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 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 run is 0, leading to division by zero in the slope formula.

Front

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

Back

Two lines are parallel if they have the same slope, meaning they rise and run at the same rate.

Front

How can you determine if two lines are perpendicular using slopes?

Back

Two lines are perpendicular if the product of their slopes is -1, meaning one slope is the negative reciprocal of the other.

Front

What is the significance of the coordinates (x1, y1) and (x2, y2) in the slope formula?

Back

The coordinates (x1, y1) and (x2, y2) represent two distinct points on a line, which are used to calculate the slope.