Question

What is the slope of a line perpendicular to the line whose equation is 4x+5y=354x+5y=35.

Answer 1

slope of perpendicular line =
`(5)/(4)`

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given the line with equation

4x + 5y = 35 ( subtract 4x from both sides )

5y = - 4x + 35 ( divide through by 5 )

y = -
`(4)/(5)` x + 7 ← in slope- intercept form

with slope m = -
`(4)/(5)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(4)/(5) )` =
`(5)/(4)`