Question

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

Answer 1

`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