Parallel and Perpendicular Lines

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 change in y divided by the change in x (rise/run).

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 'b' represent in the equation y = mx + b?

Back

In the equation y = mx + b, 'b' represents the y-intercept, which is the point where the line crosses the y-axis.

Front

What are parallel lines?

Back

Parallel lines are lines in a plane that never meet or intersect. They have the same slope but different y-intercepts.

Front

What are perpendicular lines?

Back

Perpendicular lines are lines that intersect at a right angle (90 degrees). The slopes of perpendicular lines are opposite reciprocals.

Front

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

Back

The slope of a line perpendicular to line A with slope 3 is -1/3 (the opposite reciprocal).

Front

What is the relationship between the slopes of parallel lines?

Back

The slopes of parallel lines are equal.

Front

How do you determine if two lines are parallel or perpendicular using their slopes?

Back

If the slopes are equal, the lines are parallel. If the slopes are opposite reciprocals, the lines are perpendicular.

Front

Write the equation of a line parallel to y = 2x + 3 that passes through the point (1, 5).

Back

The equation is y = 2x + 3 (same slope, different y-intercept).

Front

What is the slope of the line passing through the points (2, 3) and (4, 7)?

Back

The slope is 2, calculated as (7 - 3) / (4 - 2).