Exploring Equations of Parallel and Perpendicular Lines

The video tutorial covers the concepts of parallel and perpendicular lines, focusing on their properties and how to write equations for lines that are parallel or perpendicular to a given line. It explains that parallel lines have the same slope, while perpendicular lines have slopes that are negative reciprocals of each other. The tutorial includes examples and exercises to reinforce these concepts, concluding with a musical recap to aid retention.

What is the key property of parallel lines?

• They intersect at one point.

• They have the same slope.

• They are always horizontal.

• They form a right angle.

If two lines have the same slope, what can be said about them?

• They are perpendicular.

• They are parallel.

• They intersect at the origin.

• They are vertical.

What is the slope of a line parallel to y = 5x - 3?

• 0

• 7

• 5

• 3

Given a point (4, 7) and a line y = 5x - 3, what is the y-intercept of the line parallel to it passing through the point?

• 7

• 5

• -13

• 4

What is the defining property of perpendicular lines?

• They have the same slope.

• They never intersect.

• They are always vertical.

• They intersect to form a right angle.

What is the negative reciprocal of the slope 3?

• -1/3

• 3

• 1/3

• -3

Given a point (6, -1) and a line y = 3x + 2, what is the slope of the line perpendicular to it passing through the point?

• 1/3

• -1/3

• 3

• -3

What is the y-intercept of the line perpendicular to y = 3x + 2 passing through (6, -1)?

• -17

• 1

• -1

• 16

If two lines have slopes of -2 and 1/2, what is their relationship?

• They are perpendicular.

• They are neither parallel nor perpendicular.

• They are the same line.

• They are parallel.

Which of the following slopes would make a line perpendicular to a line with slope -1/2?

• -1/2

• 1/2

• -2

• 2