Understanding Perpendicular Lines and 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 discussing the concept of perpendicular slopes, which involves taking the negative inverse of the original line's slope. The tutorial then demonstrates how to use the point-slope form to derive the equation of the new line. Finally, it shows how to convert this equation into slope-intercept form through algebraic manipulation.

What is the first step in finding the equation of a line perpendicular to a given line?

• Identify the y-intercept of the given line

• Calculate the length of the given line

• Determine the midpoint of the given line

• Find the slope of the given line

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

• -2/5

• 5/2

• -5/2

• 2/5

What is the negative inverse of a slope of -2/5?

• 2/5

• -5/2

• 5/2

• -2/5

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

• Quadratic form

• Point-slope form

• Standard form

• Slope-intercept form

What is the point-slope form of a line that passes through (2, 8) with a slope of 5/2?

• y - 8 = 5/2(x - 2)

• y + 8 = 5/2(x + 2)

• y = 5/2x + 8

• y = 5/2x - 8

How do you convert an equation from point-slope form to slope-intercept form?

• By finding the y-intercept

• By distributing the slope and simplifying

• By changing the slope

• By calculating the midpoint

What is the slope-intercept form of the equation y - 8 = 5/2(x - 2)?

• y = 5/2x - 3

• y = 5/2x - 8

• y = 5/2x + 8

• y = 5/2x + 3

What operation is performed to both sides of the equation y - 8 = 5/2x - 5 to solve for y?

• Subtract 5

• Add 8

• Multiply by 2

• Divide by 5

What is the result of distributing 5/2 in the equation y - 8 = 5/2(x - 2)?

• 5/2x - 5

• 5/2x + 5

• 5x + 2

• 5x - 2

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

• Subtracting 3

• Adding 8

• Adding 3

• Subtracting 8