Question

write an equation of the line passing through point p that is perpendicular to the given line p(6,10),y=-3x+13

Answer 1

y =
`(1)/(3)` x + 8

Explanation:

The equation of a line in slope- intercept form is

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

y = - 3x + 13 is in this form

with m = - 3

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-3)` =
`(1)/(3)`

y =
`(1)/(3)` x + c ← is the partial equation

To find c substitute (6, 10) into the partial equation

10 = 2 + c ⇒ c = 10 - 2 = 8

y =
`(1)/(3)` x + 8 ← equation of line