what is the equation of a line that is perpendicular to -x+3y=2

Question

anonymous · Answer

there can be many lines of the form $$y+3x=c$$ where c is any constant

anonymous · Answer

First, let's isolate y (get it by itself) so the line is in slope-intercept form (y=mx+b).

-x + 3y = 2
-x + x + 3y = x + 2
3y = x + 2
3y/3 = (x + 2)/3
y = x/3 + 2/3
y = (1/3)x + 2/3
We can pull out our slope, m: 1/3.

Remember that parallel has the same slope, and perpendicular has the opposite reciprocal (flip the fraction, change the sign).

We can take 1/3 and do just that. First, we'll flip it: 3/1, which simplifies to 3. Now, we change the sign: -3. There's your slope. You can make the y-intercept (b) anything you like, but to keep it simple, it can just be 0:

y = -3x