Equations of Parallel and Perpendicular Lines

This video tutorial explains the concepts of parallel and perpendicular lines, focusing on their slopes. It provides examples to determine if lines are parallel, perpendicular, or neither. The video also covers how to write equations for lines that are parallel or perpendicular to a given line using point-slope and slope-intercept forms. Additionally, it includes problem-solving strategies for multiple-choice questions related to line equations.

What property do parallel lines share regarding their slopes?

• Slopes are negative reciprocals

• No specific slope relationship

• Slopes are unequal

• Slopes are equal

If two lines have slopes that are negative reciprocals, what is their relationship?

• They are parallel

• They are perpendicular

• They are neither parallel nor perpendicular

• They intersect at a non-right angle

What is the slope of a vertical line?

• 1

• Undefined

• -1

• Zero

In point-slope form, what does 'm' represent in the equation y - y1 = m(x - x1)?

• The y-intercept

• The x-intercept

• The distance from the origin

• The slope

Which equation represents a line parallel to the line y = 3x + 5?

• y = -1/3x - 3

• y = 1/3x + 2

• y = -3x + 1

• y = 3x - 4

What is the slope of a line perpendicular to one with a slope of 4?

• -4

• 4

• -1/4

• 1/4

If a line in point-slope form passes through (3,4) and is parallel to y = 2x + 6, what is its equation?

• y - 4 = 2(x - 3)

• y - 4 = -2(x - 3)

• y - 4 = 1/2(x - 3)

• y - 4 = -1/2(x - 3)

Which of the following is a correct method to find a line equation given a point and a parallel line?

• Use the slope of the given line and the given point in the slope-intercept form

• Use the negative reciprocal of the slope and the given point in the slope-intercept form

• Use the slope of the given line and the given point in the point-slope form

• Use the negative reciprocal of the slope of the given line in the point-slope form

What is the slope of a line perpendicular to one with a slope of -1/3?

• 3

• -3

• 1/3

• -1/3

Which option represents a line equation that passes through (5,3) and is parallel to 5x + y = 8?

• y = -5x + 28

• y = 5x - 22

• y = -5x - 22

• y = 5x + 28