Parallel and Perpendicular Lines

What is the relationship between the slopes of perpendicular lines?

• They are the same.
• They are opposite reciprocals of each other.
• They are additive inverses of each other.
• They are multiplicative inverses of each other.

What is the slope of a line that is perpendicular to the line represented by the equation y = -1/4x + 2?

• -1/4
• 1/4
• -4
• 4

What is the equation of a line that is parallel to y = 3x + 1 and passes through the point (4, 4)?

• y = 3x + 4
• y = 3x - 8
• y = -1/3x + 4
• y = -1/3x - 8

If two lines are parallel, what can be said about their slopes?

• The slopes are equal.
• The slopes are opposite.
• The slopes are reciprocal.
• The slopes are opposite and reciprocal.

In the text, what example is given to illustrate the concept of 'opposite reciprocal' in relation to the slopes of perpendicular lines?

• The lines y = 2x + 1 and y = -1/2x + 3.
• The lines y = -1/4x + 2 and y = 4x + 6.
• The lines y = 3x + 1 and y = -1/3x + 4.
• The lines y = 1/4x - 2 and y = -4x + 1.

In the text, what is mentioned as a common mistake that students can make when trying to find the equation of a perpendicular line?

• Using the same slope as the original line.
• Using the reciprocal slope, but not the opposite.
• Using the opposite slope, but not the reciprocal.
• Using the opposite and reciprocal slope, but not the correct one.

What is the final step to find the equation of a line that is parallel to another line and passes through a given point?

• Find the slope of the original line.
• Find the reciprocal slope of the original line.
• Find the y-intercept of the new line.
• Find the x-intercept of the new line.