Understanding Perpendicular Lines and Their Equations

The video tutorial explains how to find the equation of a line that is perpendicular to a given line and passes through a specific point. It begins by defining perpendicular lines and the concept of negative reciprocals. The tutorial then demonstrates how to find the slope of the perpendicular line and solve for the y-intercept using the slope-intercept form. Finally, the solution is verified graphically to ensure accuracy.

What is the main task described in the introduction of the tutorial?

• Finding the area of a triangle.

• Finding the midpoint of a line segment.

• Finding the equation of a line perpendicular to a given line.

• Finding the equation of a line parallel to a given line.

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

• They are both zero.

• They are both positive.

• They are negative reciprocals of each other.

• They are equal.

If a line has a slope of 4, what would be the slope of a line perpendicular to it?

• -4

• 4

• 1/4

• -1/4

What is the slope of the given line in the tutorial?

• 3

• -3

• 1/3

• -1/3

What is the slope of the line that is perpendicular to the given line?

• 3

• -3

• -1/3

• 1/3

Which form is used to find the equation of the perpendicular line?

• Quadratic form

• Standard form

• Slope-intercept form

• Point-slope form

What is the y-intercept of the perpendicular line found in the tutorial?

• 2

• 3

• 4

• 5

What is the equation of the line that is perpendicular to the given line and passes through the point (3, 5)?

• y = 3x + 4

• y = 1/3x + 5

• y = -3x + 4

• y = 1/3x + 4

How is the solution verified in the tutorial?

• By using a table of values

• By graphing the lines

• By checking with a calculator

• By solving algebraically

What is the significance of the intersection of the two lines in the graph?

• They do not intersect.

• They are parallel.

• They form a 90-degree angle.

• They form a 45-degree angle.