Question

Write the equation of a line perpendicular to the line: y=-(2)/(5)x that goes through the point (-8,-9).

Answer 1

y =
`(5)/(2)` x + 11

Explanation:

the equation of a line in slope- intercept form is

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

y = -
`(2)/(5)` x ← is 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)` , then

y =
`(5)/(2)` x + c ← is the partial equation

to find c substitute (- 8, - 9 ) into the partial equation

- 9 =
`(5)/(2)` (- 8) + c = - 20 + c ( add 20 to both sides )

11 = c

y =
`(5)/(2)` x + 11 ← equation of perpendicular line