Exploring Equations of Lines in Geometry

The video tutorial covers the concepts of slope, parallel lines, and perpendicular lines in the coordinate plane. It begins with a review of slope as rise over run, using both counting and formula methods. The tutorial then explains how to determine if lines are parallel by comparing slopes and introduces the concept of perpendicular lines as having slopes that are opposite reciprocals. The video includes examples and exercises to reinforce these concepts, emphasizing the importance of understanding slope in algebra and geometry.

What is the formula for calculating the slope of a line?

• y2 + y1 / x2 - x1

• x2 - x1 / y2 - y1

• x2 + x1 / y2 + y1

• y2 - y1 / x2 - x1

What is the slope of a line that goes through the points (1,3) and (2,1)?

• 2

• 1/2

• -2

• -1/2

Two lines are parallel if they have:

• Opposite slopes

• The same slope

• Different slopes

• The same y-intercept

In the slope-intercept form y = mx + b, what does 'm' represent?

• The point

• The slope

• The x-intercept

• The y-intercept

In the equation y = mx + b, what does 'b' represent?

• The slope

• The point

• The y-intercept

• The x-intercept

What is the point-slope form of a line's equation?

• x - x1 = m(y - y1)

• y - y1 = m(x - x1)

• y = mx + b

• y + y1 = m(x + x1)

Which form is used to easily write the equation of a line when you know a point on the line and the slope?

• Parallel form

• Point-slope form

• Standard form

• Slope-intercept form

How do you find a line parallel to y = 4x + 5 through the point (2, -3)?

• y = -4x - 3

• y = 4x - 3

• y = -4x + 3

• y = 4x + 3

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

• 1/4

• -1/4

• -4

• 4

If a line has a slope of 2/5, what is the slope of a line perpendicular to it?

• -5/2

• 5/2

• -2/5

• 2/5