How do you write an equation of a line given (12,3) and perpendicular to 3x-y=2?

1 Answer
Dec 15, 2017

Answer:

#y = (-1/3)x + 7#

Explanation:

take your equation #3x - y = 2# and re-write as the standard equation for a line, #y = mx + b#, where m is the slope, and b is the offset. You then have:

#y = 3x - 2#

...with slope m = 3.

The slope of the line you are trying to find is the negative inverse of this, since we're told that it's perpendicular. This slope is therefore #-1/3#.

You can then solve for the offset in the equation:

#y = (-1/3)x + b#

...you solve for b by plugging in the x value (12) that you are given on the right side, and the y value (3) that you are given on the left:

#3 = (-1/3)12 + b#

#3 = -4 + b#
#7 = b#

so your equation is #y = (-1/3)x + 7#

GOOD LUCK