Question

2. Consider the line

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

Answer 1

The slope of the perpendicular line is
`-(5)/(3)`

Explanation:

• The product of the slopes of the perpendicular lines is -1

• That means to find the slope of a perpendicular line to a given line, reciprocal its value, and reverse its sign

• Ex: If the slope of a line is
  `(1)/(3)`, then the slope of the line perpendicular to it is -3

Let us solve the question

∵ The equation of a line is y =
`(3)/(5)` x - 8

→ The form of the equation is y = m x + b, where m is the slope

∴ The slope of the line is
`(3)/(5)`

→ To find the slope of the line perpendicular to it reciprocal it and

reverse its sign

∵ The reciprocal of
`(3)/(5)` is
`(5)/(3)`

→ Change its sign from positive to negative

∴ The slope of the perpendicular line is
`-(5)/(3)`