Question

Marc is thinking of find the equation of the line through (8,1) which is perpendicular to the line y=-x/3 - 3.

Answer 1

y = 3x - 23

Explanation:

the equation of a line in slope- intercept form is

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

the given line

y = -
`(1)/(3)` x - 3 ← is in slope- intercept form

with slope m = -
`(1)/(3)`

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

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

y = 3x + c ← is the partial equation of the perpendicular line

to find c , substitute the point (8, 1 ) into the partial equation

1 = 3(8) + c = 24 + c ( subtract 24 from both sides )

- 23 = c

y = 3x - 23 ← equation of perpendicular line