Question

A line passes through points at (9,5) and (4,3). What is the slope of the line perpendicular to this line?

Answer 1

`-5/2`

Explanation:

The slope of the line through the given points is
`(5-3)/(9-4)=(2)/(5)`.

Perpendicular lines have slopes that are negative reciprocals of each other, so the answer is
`-5/2`.

Answer 2

perpendicular slope = -
`(5)/(2)`

Explanation:

calculate the slope m of the line using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (9, 5 ) and (x₂, y₂ ) = (4, 3 )

m =
`(3-5)/(4-9)` =
`(-2)/(-5)` =
`(2)/(5)`

given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((2)/(5) )` = -
`(5)/(2)`