Question

3)Write the equation of the line perpendicular to 6x + 3y = 15 that passes through the point (8, -1). Write you answer in slope-intercept form. Show ALL your work! (A) Find the perpendicular slope (B) Find the y-intercept, showing all of your work (C) Write the final equation

Answer 1

y =
`(1)/(2)` x - 5

Explanation:

A

the equation of a line in slope- intercept form is

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

given line

6x + 3y = 15 ( subtract 6x from both sides )

3y = - 6x + 15 ( divide through by 3 )

y = - 2x + 5 ← in slope- intercept form

with slope m = - 2

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-2)` =
`(1)/(2)` , then

B

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

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

- 1 =
`(1)/(2)` (8) + c = 4 + c ( subtract 4 from both sides )

- 5 = c ← the y- intercept

C

y =
`(1)/(2)` x - 5 ← equation of perpendicular line