Parallel and Perpendicular Lines

Front

What is the definition of parallel lines?

Back

Parallel lines are lines in a plane that never meet; they have the same slope.

Front

What is the definition of perpendicular lines?

Back

Perpendicular lines are lines that intersect at a right angle (90 degrees); their slopes are negative reciprocals of each other.

Front

If two lines have slopes m1 and m2, what condition must be met for the lines to be perpendicular?

Back

m1 * m2 = -1.

Front

What does the slope (m) represent in the equation of a line (y = mx + b)?

Back

The slope represents the rate of change of y with respect to x; it indicates the steepness of the line.

Front

What does the y-intercept (b) represent in the equation of a line (y = mx + b)?

Back

The y-intercept is the point where the line crosses the y-axis (when x = 0).

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

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

Front

What is the slope of the line represented by the equation y = 2x + 5?

Back

The slope is 2.

Front

If a line has a slope of 0, what can be said about the line?

Back

The line is horizontal.

Front

If a line has an undefined slope, what can be said about the line?

Back

The line is vertical.

Front

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

Back

Two lines are parallel if they have the same slope (m) in their equations.