Question

A line is perpendicular to y = -x - 1

and intersects the point (6,9).
What is the equation of this
perpendicular line?
y = [?]x + []

Answer 1

y = 2x - 3

Explanation:

the equation of a line in slope- intercept form is

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

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

with slope m = -
`(1)/(2)`

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

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

y = 2x + c ← is the partial equation

to find c substitute (6, 9 ) into the partial equation

9 = 2(6) + c = 12 + c ( subtract 12 from both sides )

- 3 = c

y = 2x - 3 ← equation of perpendicular line