Question

What is the slope of a line perpendicular to the line whose equation is 6x-15y=270

Answer 1

m= -2 1/2

Explanation:

First, let's put the equation into slope intercept form.

6x-15y=270

-15y=-6x+270

y=6/15x+270

For two lines to be perpendicular, their slopes must be opposite reciprocals.

m=-15/6 or m= -2 1/2

Answer 2

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

Explanation:

The equation of a line in slope- intercept form is

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

Given

6x - 15y = 270 ( subtract 6x from both sides )

- 15y = - 6x + 270 ( divide all terms by - 15 )

y =
`(-6)/(-15)` x - 18, that is

y =
`(2)/(5)` x - 18 ← in slope- intercept form

with slope m =
`(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)`