graphs/line equation in algebra?

Question

"write the equation of the line that passes through the given point and is perpendicular to the given line. Write the answer in point slope formula."

" (-6, 3), y + 3x = -12 "

i know that the point slope formula is y = mx + b, but i dont know the equation on how to find out if its perpendicular

Answer 1

y=-3x-12 so m=-3
For perpendicular, you need the negative reciprocal of m which is 1/3

y-3=(1/3)(x+6) is your equation, just solve for y if necessary

Answer 2

*Take the equation and set it in the slope-intercept form > y = mx+b

First: subtract 3x from both sides...

y + 3x - 3x = -12 - 3x
y = -12 - 3x

*Make sure the equation is in alpha descending order - "x" comes first ...

y = -3x - 12

*The slope is -3 but, a line with a perpendicular slope is 1/3...

Third: place the perpendicular slope and point (-6, 3) in the point-slope formula...

y - first y = m(x - first x)
y - 3 = 1/3(x - (-6))
y - 3 = 1/3(x + 6)
y - 3 = (1/3)x - (1/3)(6)
y - 3 = (1/3)x - 6/3
y - 3 = (1/3)x - 2

Fourth: isolate "y" on one side > add 3 to both sides...

y - 3 + 3 = (1/3)x - 2 + 3
y = (1/3)x + 1

Answer 3

Point-slope form is (y-a) = m(x-b), where (b,a) is the point through which the line passes. First, find the slope of the line you want:
Slopes of perpendicular lines are inverse-reciprocals of each other - i.e. slope of 2 is perpendicular to slope of -1/2. You want something perpendicular to y + 3x = -12 ==> y = -3x - 12 ==> something perpendicular to a slope of -3 ==> something with slope +1/3.
Therefore, you've got (y-3) = 1/3*(x+6)

Done.

Answer 4

y = mx + b is slope-intercept form, not point-slope form.

Any line perpendicular to y + 3x = -12 (y = -3x + 12) will have a slope of 1/3, so
(y + 6)/(x - 3) = 1/3
y + 6 = (1/3)(x - 3)

Answer 5

y+3x = -12
y = -3x -12
So the slope of the given line is -3
A line perpendicular to given line must have a slope = -1/-3 =1/3So the line perpendicular to the given line is y = 1/3x +b.
Since the line goes through(-6,3), 3 = 1/3(-6) + b so b = 5.
The desired equation is thus y = x/3 +5.