Write an equation of a line given (12,3) and perpendicular to 3x-y=2

Oscar Burton

Oscar Burton

Answered question

2022-10-29

Write an equation of a line given (12,3) and perpendicular to 3x-y=2

Answer & Explanation

Phoebe Medina

Phoebe Medina

Beginner2022-10-30Added 17 answers

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

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