Understanding Slopes of Lines

The video tutorial explains how to calculate the slope of a line passing through two points. It covers the concepts of parallel and perpendicular lines, emphasizing that parallel lines have the same slope, while perpendicular lines have slopes that are negative reciprocals. The tutorial includes a step-by-step calculation of the slope and a graphical verification of the concepts discussed.

What are the coordinates of the two points through which the line passes?

• (-3, 5) and (1, -3)

• (3, 5) and (-1, -3)

• (3, -5) and (-1, 3)

• (-3, -5) and (1, 3)

What is the formula used to calculate the slope of a line given two points?

• (x2 - x1) / (y2 - y1)

• (y2 - y1) / (x2 - x1)

• (x1 - x2) / (y1 - y2)

• (y1 - y2) / (x1 - x2)

What is the slope of the line passing through the points (-3, 5) and (1, -3)?

• -2

• 2

• 1/2

• -1/2

What is a key characteristic of parallel lines?

• They intersect at a 90-degree angle.

• They have slopes that are negative reciprocals.

• They never intersect and have the same slope.

• They have different slopes.

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

• 3/2

• -2/3

• 2/3

• -3/2

What is the relationship between the slopes of perpendicular lines?

• They are equal.

• They are negative reciprocals.

• They are both negative.

• They are both positive.

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

• -2

• 1/2

• -1/2

• 2

How do you find the negative reciprocal of a slope?

• Multiply the slope by -1.

• Subtract 1 from the slope.

• Add 1 to the slope.

• Interchange the numerator and denominator and change the sign.

What does the graphical representation of a parallel line show?

• It has the same slope as the original line.

• It has a different slope than the original line.

• It forms a 90-degree angle with the original line.

• It intersects the original line.

What does the graphical representation of a perpendicular line show?

• It has the same slope as the original line.

• It never intersects the original line.

• It has a slope of zero.

• It forms a 90-degree angle with the original line.