Question

HELP MATHS perpendicular lines

Answer 1

y =
`(1)/(3)` x + 4

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 equation of line L₁

y = - 3x + 8 ← 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 line L₂

to find c , substitute the point P(3, 5 ) into the partial equation

5 =
`(1)/(3)` (3) + c = 1 + c ( subtract 1 from both sides )

4 = c

y =
`(1)/(3)` x + 4 ← equation of line L₂