Parallel and Perpendicular Lines

Front

What are parallel lines?

Back

Parallel lines are lines in a plane that never meet. 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 negative reciprocals of each other.

Front

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

Back

Two lines are parallel if their slopes are equal. For example, in the equations y = mx + b, if both lines have the same 'm', they are parallel.

Front

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

Back

Two lines are perpendicular if the product of their slopes is -1. If one line has a slope of m1, the other must have a slope of m2 such that m1 * m2 = -1.

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

Convert the equation 6x - 8y = 5 to slope-intercept form.

Back

y = (3/4)x - 5/8.

Front

What is the slope of the line represented by the equation 5x + 2y = 8?

Back

The slope is -5/2.

Front

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

Back

The slope of the perpendicular line is -1/2.

Front

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

Back

y = 3x - 1.

Front

Write the equation of a line perpendicular to y = -1/2x + 3 that passes through the point (4, 2).

Back

y = 2x - 6.