Question

Write the equation of the line perpendicular to y=-3x-1 that passes through points (3,4)

Answer 1

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

Explanation:

the equation of a line in slope- intercept form is

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

given the line with equation

y = - 3x - 1 ← in slope- intercept form

with slope 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)` , then

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

to find c, substitute the point (3, 4 ) for x and y into the partial equation

4 =
`(1)/(3)` (3) + c = 1 + c ( subtract 1 from both sides )

3 = c

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