y = m x + b
This equation defines a straight line on a Euclidean XY coordinate system. m is the slope of the line, and b is where it intercepts the y axis. The equation is equivalent to
x = (y - b) / m
which is equivalent to
m = (y - b) / x
which is equivalent to
b = y - m x
which is also equivalent to
ey = e(m x + b)
and
ln y = ln (m x + b)
... and so on and so forth.
If you've landed on this post by Googling for "rearrange y = mx + b", might I suggest that you review your high school algebra. Seriously. If you're in a position to need to rearrange it, you shouldn't need to Google for it. -.-
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15 comments:
Oh, good. The old point-slope equation. A friend I haven't seen in a while.
I remember revisiting algebra and geometry when I was trying to create a 3D model of a buckyball!
Do I get any points at all for remembering and understanding all that?
Unfortunately, that reminded me that I actually enjoyed algebra, but there's not a lot of call for it (other than learning how to think) in my job.
Before the Googling algebraically challenged crowd gets down on themselves too bad -- it's important to realize that for many of us, such things aren't commonly used.
If I had cause to start doing point/slope stuff, I'd jump right on that Google wagon to refresh my memory.
Mind you, I am a smart guy, and scored a 4.0 in my university calc classes. I just don't use stuff like this anymore, so my brain has it neatly folded in a corner somewhere.
Brains are funny, no?
I totally agree with Shawn. I loved mathematics and especially algebra in high school and nearly scored highest grade in it (I happened to get not that good results on last exam before graduating for actually getting highest grade in the end. My usual bad luck).
Nowadays I rarely do maths so I have forgotten most of it. But I guess it would come back to me if I read some of my old school books.
I have childhood traumas from algebra...the bastards trying to drill it into my brain in the last two years of elementary school. I know it's a piece of cake...but I didn't think so at the time. Nowadays, I look fondly at the old 'point-slope' fun...statistics at university make you feel like HS and ES mathematics were fun:D
Well, see. From my view, if your web search is for "rearrange y=mx+b", that implies you actually know what the equation is for and that you have something specific you're trying to do with it (that calls for a rearrangement). Which also means you really have no excuse not knowing how to rearrange it yourself.
Either that or you are a high school student, and you're cheating. :p
Or, it was 20 years ago since you used it and only have a vague idea how to use it. And then after some refreshing of memory, you know what to do.
Can you think of an example situation like that? Where you already know the equation, what it's for, and what y, m, x, and b are all for? And yet still don't know enough algebra to solve for something other than y?
It's like suggesting that it makes sense for a chartered accountant to not have a firm grasp on basic arithmetic.
Like suggesting someone in the film industry who doesn't know what microphones look like.
Like suggesting an IT guy who doesn't know the difference between an ethernet cable and a USB cable.
My eldest son is starting college next month for theatre major, music minor.
He's seriously math impaired, and in fact will have to start below the 100 level. I realize that it's part of the package deal for a liberal arts degree, but it's really annoying that he has to take 3 math classes, 98, 99 and 140, to graduate with a degree in theatre, where he'll never use math again except to compare line counts with other cast members.
I agree that basic numeracy is just as important as literacy, but I'm not sure that algebra and trig are necessary if your career and life are pointed a different direction. I've sure never used them, not once, and I work in IT.
Well, MTW, I'm like that with some of the formulas that we used a lot in school. I know what the look like. I know what problems they were suppose to solve. But I don't remember HOW it was done. But with some reading on the net or in a math book, I'd remember again.
You probably use algebra a lot in your profession so you know how to solve the equation. It probably seems easy for you. Therefore, you might think it's natural to understand what to do.
It's like languages that you used to be good at and then after some years without using it you only understand bits of it and some words you look at and know that some time ago you knew what it meant. But now you just can't remember.
y = m x + b
y - b = m x + b - b <-- cross out both b's on right
y - b = m x
(y - b) / m = (m x) / m <-- cross out both m's on right
(y - b) / m = x
...I'll leave the other rearrangements as exercises for the student.
Sounds to me like that search was based off the wording of a math homework problem. That's where you'd see the original formula next to the word "rearrange".
Those of us who use algebra in everyday life, even infrequently, would think "oh, yeah, there's an equation for that... isn't it y = mx... oh yeah, and a sort of locator for where it is on a graph... +b... right -- y = mx + b. But wait, I have y, I need to find x. Well, if I remember my algebra right, you do the same thing to each side until you have what you need isolated on one side. Yeah, OK, so what did I say I need?" And the rearranging would be done for a specific need.
This is the difference between a cheating math student and a real life "I don't use math much, but I have to find this" situation.
Thank you, Anne!
That's what I was trying to get at. I mean, how many circumstances can there possibly be that you'd need to rearrange y=mx+b? It should be impossible to find yourself in such a situation without already knowing how to do it (or you're attempting to cheat, or you're helping someone else cheat). Otherwise you wouldn't've gotten hired to do whatever it is you're trying to do.
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