Question

A line is represented by y = -3x+6. A perpendicular line goes through (12,-2). What would be the slope intercept form for the perpendicular

line?

Answer 1

The slope-intercept form of the perpendicular line is y =
`(1)/(3)` x - 6

Explanation:

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

• If the slope of one of them is m, then the slope of the other is
  `-(1)/(m)`

The slope-intercept form of the linear equation is y = m x + b, where

• m is the slope

• b is the y-intercept

∵ The equation of a line is y = -3x + 6

→ Compare it with the form of the equation above to find m

∴ m = -3

→ Reciprocal it and change its sign to find the slope of the ⊥ line

∵ The reciprocal of -3 with the opposite sign is
`(1)/(3)`

∴ m⊥ line =
`(1)/(3)`

→ Substitute it in the form of the equation above

∴ y =
`(1)/(3)` x + b

→ To find b substitute x and y in the equation by the coordinates

of a point on the line

∵ The perpendicular line goes through (12, -2)

∴ x = 12 and y = -2

∵ -2 =
`(1)/(3)` (12) + b

∴ -2 = 4 + b

→ Subtract 4 from both sides

∴ -2 - 4 = 4 - 4 + b

∴ -6 = b

→ Subustitute it in the equation above

∴ y =
`(1)/(3)` x + -6

∴ y =
`(1)/(3)` x - 6

The slope-intercept form of the perpendicular line is y =
`(1)/(3)` x - 6