Expert: Chanda Walker - 2/25/2009

Question
Find the equation of the line that is perpendicular to 2y + x = 8 and that passes through the point (-2,-1)

Please answer asap have a test tomorow.

Answer
To find the equation of a line that perpendicular to another we have 3 steps.

1) get the original equation into the "slope-intercept form"
2) locate the slope and convert it to a perpendicular slope
3) use that new slope and the point given to find final equation


I'll demonstrate.

The original equation can be written like this with some manipulation of terms:

y = -1/2 x + 4

That is in the slope intercept form (y = mx + b).  Can you see that m = (-1/2) and b = 4.  This is a critical step.  (m is the slope, b is the intercept.)

Next, we need to grab that slope and convert it to a perpendicular slope now.  The way to do that is to invert it and multiply by -1.

So here is the equation; it looks worse than it is.

-1/m = -1/(-1/2) = 2

Ok, the slope of our new line is 2.  Let's see what our equation looks like thus far . . .

y = 2x + b

DON'T use the b from above.  We need to find a new b for our new line. To do that, we use the point given.  Substitute the point given in for the y and x and solve for b.

(-1) = 2*(-2) + b

-1 = -4 + b

b = 3

Now we are done.  Just stick that into our equation and bingo.

y = 2x + 3

Hope this helps.  Please let me know if you have further questions.