Flashcard: Distance, Midpoint, and Slope

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented as 'm' in the equation of a line (y = mx + b). It is calculated as the rise over run (change in y over change in x).

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1, meaning their slopes are opposite reciprocals.

Front

If a line has a slope of 2, what is the slope of a line perpendicular to it?

Back

The slope of a line perpendicular to a line with slope 2 is -1/2.

Front

How do you determine if two lines are parallel using their equations?

Back

Two lines are parallel if their slopes (m) are equal when the equations are in slope-intercept form (y = mx + b).

Front

What is the formula for finding the midpoint between two points (x1, y1) and (x2, y2)?

Back

The midpoint M is given by M = ((x1 + x2)/2, (y1 + y2)/2).

Front

What is the slope-intercept form of a line?

Back

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope m is calculated as m = (y2 - y1) / (x2 - x1).

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

If two lines have slopes of 3 and -1/3, what can you say about their relationship?

Back

The two lines are perpendicular because the product of their slopes is -1 (3 * -1/3 = -1).