Question

Consider the line 8x-5y=1

what is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line

Answer 1

`(8)/(5)` and -
`(5)/(8)`

Explanation:

the equation of a line in slope- intercept form is

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

given

8x - 5y = 1 ( subtract 8x from both sides )

- 5y = - 8x + 1 ( divide through by - 5 )

y =
`(8)/(5)` x -
`(1)/(5)` ← in slope- intercept form

with slope m =
`(8)/(5)`

• Parallel lines have equal slopes

then the slope of a parallel line is m =
`(8)/(5)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((8)/(5) )` = -
`(5)/(8)`