Can't Figure Out Why I Can't Figure It Out
November 19, 2010 10:05 AM   Subscribe

Warning: wait to read this question until tomorrow if you are in Learned League. So, today one of the Learned League questions was, What is the y-intercept of the line with the following equation?: 3y-11x = 39. I couldn't get any further than y = 13 + 3 2/3 x or y = 13 +3.66666x. Actually it appears the response is 13. How does one get to the right response for this question?
posted by bearwife to Education (12 answers total) 2 users marked this as a favorite
At the y intercept, x=0. Plug that into the equation and you get
3y - 11(0) = 39
3y = 39
y = 39/3
y = 13
posted by grizzled at 10:07 AM on November 19, 2010 [4 favorites]

Formula for a line is y = mx + b. m is slope, b is y-intercept. You were done at y = `11/3x + 13.
posted by Mister Fabulous at 10:09 AM on November 19, 2010 [1 favorite]

Yeah, just punch in x = 0.

3y - 11(0) = 39.

39/3 = 13.
posted by valkyryn at 10:33 AM on November 19, 2010

While both answers given above are correct (obviously), I would strongly encourage you to focus on grizzled's explanation; in fact, the key is in the first sentence: At the y intercept, x=0.
Draw an x-y graph with some line (any line, it does not have to be 3y-11x=39) going through it. Understand the relation between the expressions "y intercept" and "x=0".

Memorizing and equation and names of coefficients, like Mister Fabulous quotes, is great if you have a very good memory ... but I always tell students: focus on understanding, not memorizing.
posted by aroberge at 10:33 AM on November 19, 2010 [3 favorites]

Mister Fabulous's response is good once you understand that what grizzled said is true. And to follow up on what aroberge said, if you'd like to easily see what it looks like graphed, here is 3y-11x=39 on WolframAlpha.
posted by asciident at 10:45 AM on November 19, 2010 [1 favorite]

Understanding the grizzled answer is helpful because it would apply to equations that aren't lines as well.
posted by advicepig at 10:58 AM on November 19, 2010 [1 favorite]

Many thanks to all of you. I think this is the first time I understood the graphing concepts at issue -- and it is nice to have that happen sometime in my life.
posted by bearwife at 11:00 AM on November 19, 2010

For what it's worth (I'm late to the party), the words "x-intercept" and "y-intercept" actually do tell you what to do, if you think about it carefully.

Think about the line lying there on the x-y plane. It's going to cross the x-axis and the y-axis (well, usually). Another name for cross is intersect---or, even, intercept.

So the "y-intercept" is a fancy name for "where does the line intersect the y-axis"?

Well, it intersects the y-axis exactly when x = 0.

(Moreover, if the question had asked about the x-intercept instead, then the question would really be asking "where does the line intersect the x-axis"? Well, the x-axis is where y = 0, so in this case you'd plug in y = 0 to the equation and get x= -39/11.)
posted by leahwrenn at 11:12 AM on November 19, 2010 [1 favorite]

An Older School way of solving these graph-a-function problems is/was to to take easy values for x & y ("0" is an easy value, as is "1", and "-1"), and plot it out (in the process of doing this for more complex functions, you learn the general shapes).

Nowadays, the solution step process taught is something like: draw the basic function shape (in this case, a line), then correct (do transformations) for negative signs, inversions, etc.

This newer method pretty much baffled some not-yet-40ish engineering types when a co-worker came in asking "can you explain this so my daughter can pass her math class?" -- much like many parents were baffled with the New Math introduced in the 1960s. All this to say: if you were imprinted with a different method than the one used in Learned League, you may find some topics seemingly harder than they should be. Don't be reluctant to look at other materials -- there's more than one way to skin a cat solve an equation (where "solve" means understand), and a lesson that will resonate with one student will be opaque to another.
posted by Tuesday After Lunch at 11:18 AM on November 19, 2010

But I'm kind of tearing my hair out here, because shouldn't 13 be obvious by inspection??

There used to be a step before graphing which which was "look at the equation for potentially trivial solutions"...and 39 is pretty obviously divisible by 3.

(No disrespect meant by this comment, bearwife.)
posted by MisterMo at 11:18 AM on November 19, 2010

I cannot favorite aroberge's comment enough times. There is wisdom in those words.
posted by King Bee at 11:41 AM on November 19, 2010

But I'm kind of tearing my hair out here, because shouldn't 13 be obvious by inspection??

Yes, if I'd remembered that x had to be zero! Sadly, I got into trying to solve this with basic algebra instead, and then all I could think to do was describe y in terms of its relationship to x.

But happily, now I see much better than before how an algebraic equation can describe a line or other shape on a graph. So I learned something, always a great outcome for an AskMeFi question.
posted by bearwife at 3:57 PM on November 19, 2010

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