I'm tutoring a friend in college algebra. She probably one of the most anal people (structured) I know, yet she cannot get basic college algebra. I've explained that one must follow the rules. She is learning graphing...basic Y= mx+b. She doesn't understand that b = y - intercept. Why doesn't y = y - intercept? m = slope but why doesn't x = x intercept? Arrrgh! HELP!

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Insanity: doing the same thing over and over again and expecting different results.
Albert Einstein

Maybe try to explain that "y" is the y-coordinate of any point on the graph, while "x" is the x-coordinate.

So, the equation tells you what the x value for any y is (and vice versa), or tell you both if you know the slope and a point, etc.

I dunno, it might work. :-|

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Make sure she understands what 'intercept' means. MANY people have less trouble with math than with the specialized lingo of math.

y = mx + b

y - mx = b

y - intercept = b

That last jump can easily confuse people. Why is 'mx' the same as 'intercept'?

After almost 50 years I still can't keep 'ordinate' and 'abscissa' straight.

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If they can get you asking the wrong questions, they don't have to worry about the answers.

I like G-Dwarf's answer. (Not that Mike's is bad, either.) One of the most elementary hurdles I see with symbolic math is realizing that variables can have any value. I'm guessing you've tried to show her that, for fixed m and b, y and x can be any of many different pairs of values? (That's where I'd start.)

Took me a day: keep them in alphabetical order, same as x and y.

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0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 ...

Thanks, but over the years I have come to treasure my ignorance.

But those two also tend to make my point. Why confuse a math newbie with ordinate and abscissa when 'x-coordinate' and 'y-coordinate' are much more self-explanatory? Especially when 'abscissa' sounds like an infected tooth?

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If they can get you asking the wrong questions, they don't have to worry about the answers.

I'm with Mike. I didn't know the meaning of the words until 01101001's post. I can't even remember (or keep straight) "numerator" and "denominator" half the time. (Being as my Astro 101 student's hate inverse-square laws, I don't care too much at the moment. )

This may not be the problem, but could be:

The symbol used for the minus sign is ambiguous, and the term
"intercept" is not handled consistently.

b = y - intercept

Does that mean

b equals y minus the y intercept?

b equals y minus the x intercept?

b equals the y-intercept?

-- Jeff, in Minneapolis

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http://www.FreeMars.org/jeff/

"I find astronomy very interesting, but I wouldn't if I thought we
were just going to sit here and look." -- "Van Rijn"

"The other planets? Well, they just happen to be there, but the
point of rockets is to explore them!" -- Kai Yeves

Perhaps we'll spend some time going over the vocabulary. Then, I'll have her graph a line and take different points on the line and plug in the x and y. I think she may see all those letters in the equation and just freaks out.

She really had a tough time with integers, negative integers. She kept saying you can't have less that nothing. I finally made a fake checkbook ledger and showed how an account can have less than zero dollars, a negative balance.

What is a real world application for y = mx + b?

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Insanity: doing the same thing over and over again and expecting different results.
Albert Einstein

That seems very likely.

I teach maths, mainly to adults, and mainly at a fairly low level and in a real-world context.

The people I teach are not stupid, but aspects of maths genuinely scare them. A mix of letters and numbers can, as you say, freak them out.

Recently I tackled this by showing them a "scary" equation:

T = 40W + 30

Once I'd given them time to make guesses as to its meaning (one thought "40W" meant a 40 Watt light bulb, which is not an unreasonable guess) I explained that it was something a lot of them have probably done for a Sunday lunch.

For cooking a certain kind of meat, T is the time in minutes, and W is the weight in kilograms.

I was hoping this would make equations less scary, and to some extent I think it worked.

The main problem, I believe, is that if you do know some maths, it is very hard to think yourself into the mindset of those who simply don't. One student asked me if the letters in algebra have values - "Is it, like, A is 1, B is 2 and so on?" Another time, I was trying to explain pi, but one student thought I'd written a capital T followed by a small i - Ti - and she couldn't understand why I was apparently calling it "pie"!

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Nothing beautiful was ever made from gravel.

I thought of Motor Oil. 40W(weight) 30 (viscosity).

heh...


Tenzoil.

So, you're coming to Minnesota and staying with me for the summer?

I'm not 'scared' of or 'freaked out' by equations, but I am averse to
them. When I come to them in text, I want to skip over them and
continue reading. It's like going for a walk, but then coming upon a
60-pound backpack I'm supposed to carry. No, I'll just leave the
backpack sitting there.

More than two variables in an equaton, and it begins to look like a
jumble-- like the dies from a Scrabble game and a numerical game
have been dumped out together at random on the page.


I helped a guy who was studying for a GED. Fractions. I gave
him some fractions to add, and the first one, involving 1/4, worked
fine. But the rest didn't go so well. It turned out that he thought
"one quarter" was 25 cents, so he added .25 in the first problem
and got the right answer.

-- Jeff, in Minneapolis

__________________
http://www.FreeMars.org/jeff/

"I find astronomy very interesting, but I wouldn't if I thought we
were just going to sit here and look." -- "Van Rijn"

"The other planets? Well, they just happen to be there, but the
point of rockets is to explore them!" -- Kai Yeves

You're having some work done on your computer. The service guy charges a $100 basic charge just to come out, plus $20 an hour for however long it takes. How much will it cost you if he comes out and works 8 hours?

y = final cost.
m = $20, the per-hour charge
x = 8, the number of hours worked
b = $100, the upfront charge.

y = mx + b
y = 20*8 + 100
y = 160 + 100
y = 260

An eight-hour job will cost you $260 dollars.

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SeanF

"Ask to understand, but don't challenge unless you have the knowledge."--NEOWatcher

The contents of this post are ©2009 by SeanF and may not be copied or retransmitted in any form without the express written consent of SeanF

That's a good example, SeanF. Have her calculate the cost for different x (hour) values and graph it. She'll see that b ($100) is the y intercept. That'll help reenforce the concept.

All good examples.

I come back to specialized meanings of words and just now asked myself 'The intercept of what?" Why is it special?

I'm at least half-convinced that much of the problem many people have learning basic mathematics has lss to do with the math and more to do with len language.

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If they can get you asking the wrong questions, they don't have to worry about the answers.

Last time I saw y = mx + b was in 1998-99. I miss my old TI-82, because while the rest of the class was graphing functions, I was playing space-invaders and missle-defense which I had programmed myself.

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I'm like one of those idiot savants...well, except for the savant part.
"In order to increase awareness of the homeless, security have been given binoculars."

Should be very easy to explain if you agree on the definition of „intercept“:
y- intercept = value of y at x=0, which of course is y-intercept=m*0 +b = b
x-intercept = value of x at y=0, which is 0=m*x-intercept+b, or x-intercept = -b/m

Is that what you were asking for? Is it of any help?

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If everyone had even a basic grasp of scientific principles, this planet would be a better place (Phil Plait)

Die Lücke, die wir hinterlassen, ersetzt uns vollkommen [The gap we will leave behind will take our place entirely] (Carl Heinz Schroth)

1 + e^i*pi = 0

From the questions you write, I would say that you need to insist on a couple of ideas with her:

1. In analytic geometry, equations such as y=mx+b are a shorthand way of describing curves.
   
2. The letters m and b are constants, but the letters x and y stand for arbitrary numbers. Make sure she grasps the difference between a symbolic constant and a variable, which can be subtle at first. Constants represent fixed values which we may not care to specify. Variables represent all possible values in a certain range. Context matters here, alas.
   
3. We interpret each particular pair (x, y) as the coordinates of a point in a cartesian system (if she is completely new to this, reminding her of the battleship game might be helpful here). The equation y=mx+b is supposed to represent all the points in the line at once. It's a "test" we do to check whether some point in the plane belongs to the line or not. Particular pairs (x, y) which verify the equality y=mx+b fall along the line; points which do not verify the equality fall outside it. (A more suggestive notation might be (x₀, y₀); in any case, try to get her used to both notations, and to switching between equivalent notations.)

On a final note, I was not familiar with the term "y-intercept". I've only ever heard "intercept". Is it standard in English?

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"A witty saying proves nothing" Voltaire.
"All your bias are belong to us" Ara Pacis.

I like a little more directly applicable equation

you have $20, lunch costs $8, How much gasoline can you buy to get home?

Once you get their brain working, they should figure it out, but if you write:

y=3x+8
and y=20, find x

They wont figure it out.

Len Language? Sounds like a character in a PBS Kids educational cartoon.

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Relight the Firefly!

"It is quite clear that Occam's razor does not sharpen in your pyramid." (Nicolas)

"Still, a man hears what he wants to hear and disregards the rest." (Paul Simon)

As I learned it, the y-intercept is the value of y when x is zero, and the x-intercept is the value of x when y is zero. In other words, they're the points where the graph of the function crosses the axes.

A well-formed function in one variable can have only one y-intercept (or none, if it's not defined for x = 0), but could have none, one, or many x-intercepts. There's an interesting branch of applied math that is concerned with finding those roots computationally. It's not always easy.

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Relight the Firefly!

"It is quite clear that Occam's razor does not sharpen in your pyramid." (Nicolas)

"Still, a man hears what he wants to hear and disregards the rest." (Paul Simon)

Thanks for the explanation. It might be worth noting to Tinaa's friend that, when studying straight lines, "y-intercept" is often shortened to just "intercept". The Excel spreadsheet uses this terminology, for instance. This is because the y-intercept appears explicitly in the equation y=mx+b (it's b).

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"A witty saying proves nothing" Voltaire.
"All your bias are belong to us" Ara Pacis.

Len Language is a subset of Leg Language, spoken on the northeast corner of the Isle of Wight between Ryde and Sandown, facing Hayling Island.

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If they can get you asking the wrong questions, they don't have to worry about the answers.

A dialegt, so to speak.

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Nothing beautiful was ever made from gravel.

With enough effort, we can hijack any thread we choose.

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If they can get you asking the wrong questions, they don't have to worry about the answers.

I was told (or read) once that the best teachers are those who struggled themselves in school. The person who knows a subject so well that s/he "gets it" the first time will know only one way to teach that subject; the person who has to work to get it will find several approaches and will later have several ways of teaching it.

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Never attribute to malice what can be adequately explained by ignorance or stupidity.
Isaac Asimov

Thanks for all the help. I had a very rough time in HS algebra. Went to college a few years later and it all made sense. I've got several different ways to try now.

__________________
Insanity: doing the same thing over and over again and expecting different results.
Albert Einstein

Kinematics, for instance.

Conversion between Celsius, Kelvin, and Fahrenheit degrees.

There are plenty of examples.

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"A witty saying proves nothing" Voltaire.
"All your bias are belong to us" Ara Pacis.

I'm noticing the same thing now that I'm (really) teaching physics and astronomy courses.

Again, my opinion, but one of the greatest dangers (mentioned above) is someone who knows the subject so well it can be dificult to empathize with a person struggling with basic stuff and getting a MEGO. As a example (and I'm NOT picking on anyone here)

Show that in print to a neophyte and heads, or at least eyes, will roll. Not that it is wrong (looks right to me). But it's unreadable. It makes my own eyes hurt even while agreeing.

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If they can get you asking the wrong questions, they don't have to worry about the answers.