Writing Equations of Parallel and Perpendicular Lines

This video tutorial covers the concepts of parallel and perpendicular lines, focusing on their properties and how to determine if lines are parallel or perpendicular based on their slopes. The lesson includes practice problems to reinforce understanding and concludes with a method to verify if a triangle is a right triangle using slopes.

What are parallel lines?

• Lines that have different slopes

• Lines in the same plane that do not intersect

• Lines that intersect at multiple points

• Lines that intersect at right angles

Which of the following is true about the slopes of parallel lines?

• They intersect at right angles

• They have different slopes

• They have negative reciprocal slopes

• They have the same slope

Given the equations y = 2x + 7 and y = 2x - 1, what can be said about these lines?

• They are perpendicular

• They are the same line

• They are parallel

• They intersect at one point

What must be true for two lines to be perpendicular?

• They have the same slope

• They are in different planes

• Their slopes are negative reciprocals

• They have different y-intercepts

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

• 3

• -3

• 1/3

• -1/3

Determine if the lines y = 2/3x + 5 and y = -3/2x + 1 are parallel or perpendicular.

• Both

• Parallel

• Perpendicular

• Neither

Write the equation of a line that passes through (-3, 2) and is parallel to y = 4/7x + 5.

• y = 4/7x + 26/7

• y = 4/7x + 5/4

• y = 4/7x + 2

• y = 4/7x + 3

What is the slope of a line perpendicular to y = 4/7x + 5?

• 4/7

• -4/7

• -7/4

• 7/4

Determine if the lines passing through the points (2, -4) and (-2, 2) are parallel or perpendicular to the lines passing through (3, 6) and (5, 3).

• Both

• Perpendicular

• Parallel

• Neither

Use the slopes of the line segments to show that ABC is a right triangle if AB has a slope of -1/2 and BC has a slope of 2.

• Yes, they are parallel

• No, they are not perpendicular

• Yes, they are perpendicular

• No, they are parallel