Question

8b. Find the equation of the line perpendicular to y=-(2)/(5)x-7 that goes through (6,-2)

Answer 1

y =
`(5)/(2)` x - 17

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 - 7 ← 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 the coordinates of the point (6, - 2 ) into the partial equation.

- 2 =
`(5)/(2)` (6) + c = 15 + c ( subtract 15 from both sides )

- 17 = c

y =
`(5)/(2)` x - 17 ← equation of perpendicular line