Question

What is the equation for a line perpendicular to y=3x+5 that passes through the point (3, 1)?

Answer 1

y = -
`(1)/(3)` x + 2

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 + 5 ← 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)` , then

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

to find c, substitute the point (3, 1 ) for x and y into the partial equation

1 = -
`(1)/(3)` (3) + c = - 1 + c ( add 1 to both sides )

2 = c

y = -
`(1)/(3)` x + 2 ← equation of perpendicular line