Perpendicular Lines and Their Slopes

This video tutorial teaches how to identify and write equations of perpendicular lines by understanding their slopes and y-intercepts. It explains the slope-intercept form and how perpendicular lines have slopes that are opposite reciprocals. The tutorial includes examples of determining if lines are perpendicular and writing equations for lines that are perpendicular to a given line. It also applies these concepts to solve geometry problems involving perpendicular lines on a coordinate plane.

What is the general form of a linear equation in slope-intercept form?

• y = a/x + b

• ax + by = c

• y = ax^2 + bx + c

• y = mx + b

What is the relationship between the slopes of two perpendicular lines?

• They are both undefined.

• They are equal.

• They are opposite reciprocals.

• They are both zero.

If a line has a slope of 1/2, what is the slope of a line perpendicular to it?

• 2

• 1/2

• -2

• -1/2

How do you convert the equation 2x + 3y = 9 to slope-intercept form?

• y = -2/3x + 3

• y = 3/2x + 9

• y = 2/3x + 3

• y = -3/2x + 9

What is the opposite reciprocal of the slope -2/3?

• -3/2

• 3/2

• -2/3

• 2/3

What is the slope of the line perpendicular to y = 1/5x + 8?

• 1/5

• 5

• -5

• -1/5

Which form is used to write the equation of a line given a point and a slope?

• Quadratic form

• Point-slope form

• Standard form

• Slope-intercept form

What is the equation of a line perpendicular to y = -4x + 2 and passing through (8, 12)?

• y = 1/4x + 10

• y = -4x + 10

• y = 4x + 10

• y = -1/4x + 10

In the context of the video, what is the significance of the y-intercept when determining if two lines are perpendicular?

• It must be different for both lines.

• It does not affect perpendicularity.

• It must be zero for both lines.

• It must be the same for both lines.

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

• 1/4

• -1/4

• 4

• -4