Write the equation of the line which passes through (8, 1) and is perpendicular to x = 4x-2

Question

nosnip · Answer

and how can i work it out please?

e.mccormick · Answer

Do you know the relationship between the slope of a line and any line perpendicular to it?

nosnip · Answer

only that if it's a fraction the fraction is sort of flipped :/

e.mccormick · Answer

VERY CLOSE!  You forgot the negative sign.

nosnip · Answer

okay, what do i do to work it out though?

e.mccormick · Answer

They are negative inverses.  So if the slope of a line is $m$ then the slope of a line perpendicular to it will be $-\frac{1}{m}$

So if it is a fraction, it would be flipped and negative.  That is where we start. What is the slope of your given line?

nosnip · Answer

4 so would the gradient be 1/4 or .25?

nosnip · Answer

-1/4 or -0.25 i mean

e.mccormick · Answer

YES!  So, you have a slope and you were given the point (8,1).  Do you know the point-slope formula?

nosnip · Answer

no

e.mccormick · Answer

Ah, that is the key here:  $y-y_1=m(x-x_1)$
Ever seen that?

nosnip · Answer

yes i think so

e.mccormick · Answer

Well, you take your point and set it to the sub one versions.  So: $(8,1)=(x_1,y_1)$ Can you put those in the right place in the formula now?

nosnip · Answer

what would the other y and x be? i mean the ones that aren't x1 or y1?

e.mccormick · Answer

Just the letters.

nosnip · Answer

oh okay would it be    y-1 = -0.25(x-8)

e.mccormick · Answer

Great!  Now simplify it and get the y alone.  Know what I mean?

nosnip · Answer

yep, give me a minute :)

nosnip · Answer

would it be y= -0.25-1

e.mccormick · Answer

What happned to the x?  And you have $-\frac{1}{4}$ distributing to -8... so not 1.

e.mccormick · Answer

Oh, or did you forget the sign on the -1 when you moved it from the left to the right?

e.mccormick · Answer

Hmmm... or some sign issue.

nosnip · Answer

don't you add 1 if i move it from one side to the other?

e.mccormick · Answer

Yah, but $-\frac{1}{4}\times -8=??$

nosnip · Answer

that would be -2 so i went from y-1 =-0.25x - 2    to   y=-0.25x-1 because i added the 1

e.mccormick · Answer

Why would a negative times a negative be a negative?

nosnip · Answer

oh yes! i forgot the - on the 8 okay then it would be =3

nosnip · Answer

i mean +3

e.mccormick · Answer

/cheer

nosnip · Answer

so y = -0.25x+3

e.mccormick · Answer

Yes, or $y=-\frac{1}{4}x+3$ if you like fractions.  (Fractions are your friends! Really!)

nosnip · Answer

okay cheers :)

e.mccormick · Answer

The - sign is like pants.  Embarrassing when you drop them at the wrong time.  But once we got past that, it all came together.

nosnip · Answer

haha great thanks :)

e.mccormick · Answer

There is one other thing to be very careful of when you use the point slope formula.  It is another sign problem.  Want to see what I mean?

nosnip · Answer

yes please

e.mccormick · Answer

OK, what if I took the same line, but I wanted a perpendicualr at (-1,-6)?

nosnip · Answer

the minuses would make positives  y+6 = -1/4(x+1) ?

e.mccormick · Answer

My $(x_1,y_1)=(-1,-6)$ So when I put them into $y-y_1=m(x-x_1)$ I have to watch out for the sign!

$y-y_1=m(x-x_1)\implies (y-(-6)=m(x-(-1))$ and yah, you caught on.

nosnip · Answer

woohoo :)

e.mccormick · Answer

So that is the other sneaky sign problem to watch out for with these.  If you can get down the formula, you should do fine.

nosnip · Answer

great thanks so much!

e.mccormick · Answer

no problem!  Have fun!