Perpendicular Lines and Slope Concepts

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 with a review of perpendicular lines and their slopes, which are negative reciprocals. The tutorial then demonstrates how to convert the given line's equation into slope-intercept form to find its slope. Using this slope, the negative reciprocal is calculated to determine the slope of the perpendicular line. The point-slope form is used to find the equation of the perpendicular line, which is then converted into slope-intercept form. Finally, the solution is verified graphically to ensure accuracy.

What is the goal of the problem discussed in the video?

• To find the slope of a given line.

• To find the intersection point of two lines.

• To find the equation of a line perpendicular to a given line and passing through a specific point.

• To find the equation of a line parallel to a given line.

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

• They are equal.

• They are negative reciprocals of each other.

• They are both zero.

• They are both undefined.

If a line has a slope of 2/3, what is the slope of a line perpendicular to it?

• 3/2

• -2/3

• -3/2

• 2/3

What is the first step in converting the equation X - 4Y = 15 to slope-intercept form?

• Add X to both sides.

• Subtract X from both sides.

• Divide both sides by 4.

• Multiply both sides by 4.

What is the slope of the line given by the equation X - 4Y = 15?

• -4

• 4

• -1/4

• 1/4

What is the slope of a line perpendicular to a line with a slope of 1/4?

• 4

• -4

• 1/4

• -1/4

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

• General form

• Point-slope form

• Slope-intercept form

• Standard form

What is the equation of the line that is perpendicular to X - 4Y = 15 and passes through the point (3, 1)?

• Y = -4X - 13

• Y = 4X + 13

• Y = -4X + 13

• Y = 4X - 13

What is the final step in converting the point-slope form to slope-intercept form?

• Multiply both sides by the slope.

• Add the y-coordinate of the point to both sides.

• Subtract the y-coordinate of the point from both sides.

• Distribute the slope and simplify.

What does the graphical verification confirm about the two lines?

• They intersect and form a right angle.

• They do not intersect.

• They have the same slope.

• They are parallel.