Writing Equations of Parallel and Perpendicular Lines

This video tutorial covers writing equations of parallel and perpendicular lines. It begins with a review of the definitions and properties of parallel and perpendicular lines, focusing on their slopes. The concept of opposite reciprocal slopes is explained with examples. The tutorial then compares slopes to determine if lines are parallel, perpendicular, or intersecting. It also demonstrates using the slope-intercept form to find slopes and write equations for lines parallel or perpendicular to a given line.

What is the defining characteristic of parallel lines?

• They intersect at right angles.

• They are always vertical.

• They never intersect.

• They have different slopes.

How are the slopes of perpendicular lines related?

• They are equal.

• They are both positive.

• They are opposite reciprocals.

• They are both negative.

If a line has a slope of 3/4, what is the slope of a line perpendicular to it?

• 4/3

• 3/4

• -3/4

• -4/3

What is the slope of a line perpendicular to a line with a slope of 0?

• Undefined

• -1

• 1

• 0

Given points (2, 3) and (5, 7), what is the slope of the line passing through them?

• 4/3

• 2/3

• 1

• 1/2

If two lines have slopes of 2/5 and -5/2, what is their relationship?

• Coinciding

• Neither

• Perpendicular

• Parallel

What is the slope of the line represented by the equation y = 3x + 4?

• -3

• -4

• 4

• 3

How do you find the slope of a line from its equation in slope-intercept form?

• Look at the coefficient of x.

• Subtract the y-intercept from x.

• Look at the constant term.

• Divide the y-intercept by x.

What is the equation of a line parallel to y = 2x + 3 that passes through the point (1, 4)?

• y = 2x + 1

• y = 2x + 4

• y = 2x + 2

• y = 2x + 5

What is the equation of a line perpendicular to y = -3x + 2 that passes through the point (2, -1)?

• y = -1/3x - 5/3

• y = 1/3x + 5/3

• y = -1/3x + 5/3

• y = 1/3x - 5/3