Equations of Parallel and Perpendicular Lines

This video tutorial covers the concepts of parallel and perpendicular lines, explaining how to write equations for lines in point-slope form that are parallel or perpendicular to a given line. It includes definitions, properties, and examples of both types of lines, emphasizing the importance of slope and y-intercept. The tutorial also guides viewers on determining whether two lines are parallel, perpendicular, or neither by comparing their slopes.

What is the defining characteristic of parallel lines?

• They intersect at multiple points.

• They have different slopes and the same y-intercept.

• They have the same slope but different y-intercepts.

• They intersect at a right angle.

Given the equations y = 1/2x + 1 and y = 1/2x - 3, what can be said about these lines?

• They are perpendicular.

• They are parallel.

• They are neither parallel nor perpendicular.

• They are the same line.

How do you determine the slope of a line given in slope-intercept form y = mx + b?

• The slope is the y-intercept.

• The slope is the coefficient of x.

• The slope is the constant term.

• The slope is the product of m and b.

What is the slope of a line that is perpendicular to a line with a slope of 2?

• -2

• 1/2

• 2

• -1/2

If a line passes through the point (2, 4) and is perpendicular to the line y = 1/3x - 1, what is the slope of the new line?

• 1/3

• -1/3

• -3

• 3

What is the product of the slopes of two perpendicular lines?

• -1

• 1

• 0

• Undefined

Given the equations y = 4/5x - 8 and 4y = -5x + 12, are these lines parallel, perpendicular, or neither?

• Neither

• Parallel

• Cannot be determined

• Perpendicular

What must be true for two lines to be considered parallel?

• They must intersect at a right angle.

• They must have opposite slopes.

• They must have the same y-intercept.

• They must have the same slope.

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

• They are parallel.

• They are neither parallel nor perpendicular.

• They are perpendicular.

• They are the same line.

Given the equations y = 3/4x + 7 and 4x - 3y = 9, are these lines parallel, perpendicular, or neither?

• Cannot be determined

• Parallel

• Perpendicular

• Neither