Question

Does someone mind helping me with this problem? Thank you!

Answer 1

Below

Explanation:

Point slope form of the new line would be

(y -2) = m (x-3) from the given formula

From the GIVEN line....its slope, m , is 1/2

perpendicular slope is - 1/m = -2 ( this is something you have to remember/learn)

then the NEW Line becomes

(y-2) = -2 ( x-3) expand and simplify

y-2 = -2x+ 6

y = -2x + 8 Done !

Answer 2

y = - 2x + 8

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 - 9 ← is in slope- intercept form

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

given a line with slope m then 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 the point (3, 2 ) into the partial equation

2 = - 2(3) + c = - 6 + c ( add 6 to both sides )

8 = c

y = - 2x + 8 ← equation of perpendicular line