Exploring Equations of Parallel and Perpendicular Lines

The video tutorial explains how to write the equations of lines that are parallel and perpendicular to a given line. It begins with an introduction to the concepts of parallel and perpendicular lines and their equations. The tutorial then provides a step-by-step guide on using the point-slope formula to write the equation of a line parallel to a given line, emphasizing the importance of using the same slope. It continues with instructions on writing the equation of a line perpendicular to a given line, highlighting the need to flip the slope and change its sign. The tutorial concludes with examples and tips for solving these equations.

What is the relationship between the slopes of parallel lines?

• They are perpendicular.

• They are negative reciprocals.

• They are zero.

• They are equal.

Given the line y = 2x + 3, what is the slope of a line parallel to it?

• 2

• 3

• -2

• 1/2

Which formula is used to write the equation of a line when a point and slope are known?

• Quadratic form

• Standard form

• Point-slope form

• Slope-intercept form

What is the equation of a line parallel to y = 2x + 5 passing through the point (2, 4)?

• y = 2x + 8

• y = 2x + 0

• y = 2x - 4

• y = 2x + 4

In the point-slope formula, what does the 'm' represent?

• The x-coordinate

• The slope

• The y-coordinate

• The y-intercept

What is the first step in writing the equation of a line given a point and a slope?

• Convert to standard form

• Find the y-intercept

• Use the point-slope formula

• Graph the point

If a line has a slope of 1/4, what is the slope of a line perpendicular to it?

• -4

• 4

• -1/4

• 1/4

What happens to the slope when finding a line perpendicular to another line?

• It remains the same.

• It is doubled.

• It is flipped and the sign is changed.

• It is halved.

What is the equation of a line perpendicular to y = 1/4x + 6 passing through the point (2, -3)?

• y = -4x + 11

• y = 4x + 11

• y = 4x - 11

• y = -4x - 11

What is the result of distributing the slope in the point-slope formula?

• A quadratic equation

• A linear equation

• An undefined value

• A constant value