Parallel and Perpendicular Slopes and Line Equations

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, regardless of how far they are extended.

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 they intersect at a right angle.

Front

What is the slope-intercept form of a line?

Back

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

Front

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

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the equation of a vertical line?

Back

The equation of a vertical line is of the form x = a, where 'a' is a constant. Vertical lines have undefined slopes.

Front

What is the equation of a horizontal line?

Back

The equation of a horizontal line is of the form y = b, where 'b' is a constant. Horizontal lines have a slope of 0.

Front

If a line has a slope of 3, what is the slope of a line perpendicular to it?

Back

The slope of a line perpendicular to a line with a slope of 3 is -1/3, as perpendicular slopes are opposite reciprocals.

Front

What is the relationship between the slopes of parallel lines?

Back

The slopes of parallel lines are equal; they have the same value.

Front

How can you determine if two lines are parallel from their equations?

Back

Two lines are parallel if their equations have the same slope when expressed in slope-intercept form (y = mx + b).