Understanding Perpendicular Lines and Slope

The video tutorial explains how to find the equation of a line that passes through a given point and is perpendicular to a specified line. It covers the concept of perpendicular lines, the calculation of the opposite reciprocal slope, and the use of the point-slope form to derive the equation. The tutorial concludes with solving the equation to find the final line equation.

What is the first step in solving the problem of finding a perpendicular line?

• Identifying the slope of the given line

• Finding the y-intercept

• Sketching the graph

• Determining the coordinates of the point

What does it mean for two lines to be perpendicular?

• They have the same y-intercept

• They intersect at a right angle

• They have the same slope

• They are parallel

How do you sketch the graph of the line y = -5/3x - 8?

• By finding the x-intercept

• By using the midpoint formula

• By plotting points and drawing a line through them

• By using the slope and y-intercept

What is the slope of the line perpendicular to y = -5/3x - 8?

• -3/5

• -5/3

• 5/3

• 3/5

What is the opposite reciprocal of -5/3?

• 3/5

• -5/3

• -3/5

• 5/3

Which form of the equation is used to find the line passing through a given point with a known slope?

• Quadratic form

• Point-slope form

• Slope-intercept form

• Standard form

What is the point-slope form of the equation for a line passing through (-9, -3) with a slope of 3/5?

• y + 3 = 3/5(x + 9)

• y - 3 = 3/5(x - 9)

• y - 9 = 3/5(x - 3)

• y + 9 = 3/5(x + 3)

What is the next step after applying the point-slope form to the equation?

• Simplifying the equation

• Finding the y-intercept

• Plotting the graph

• Finding the x-intercept

How do you simplify the equation y + 3 = 3/5(x + 9)?

• By distributing 3/5 and then subtracting 3

• By adding 3 to both sides

• By multiplying both sides by 5

• By dividing both sides by 3

What is the final equation of the line that is perpendicular to y = -5/3x - 8 and passes through (-9, -3)?

• y = -3/5x - 9/5

• y = 3/5x - 9/5

• y = -3/5x + 9/5

• y = 3/5x + 9/5