Math help: finding equation in standard form for line with no slope

[quark]

I keep tripping myself up with this one...I know I am missing something. How would you show your work for

 

Find an equation in standard form for the line described: passing through the origin with no slope.

 

I know the answer is x=0. Just trying to figure out best way/ accurate way to show my work.

 

I'm consulting AoPS Intro to Alg ch 8 and I don't see steps written out, only explanation in a short paragraph form.

 

Trying to refresh/ review my algebra. :P

[wapiti]

what's "no slope"?  is the slope zero (y=0) or is the slope undefined (x=0) ?  If this is a problem in aops, please post the number so I can look at their solution :).  

 

But yes, I'd be irked if I had to show work for that too, though it can be done, just a lot of zeros involved... ( y = 0(x) + 0 ?)

[Arcadia]

I went from y = mx + c (slope intercept form) to Ax + By = C (standard form)

c = 0 (pass through origin)

m = 0 (no slope)

y = 0

0x + y = 0

Think I need another round of coffee.

[quark]

No slope here means undefined me thinks. It's from Dolciani's Alg2 and I'm using AoPS as a supplement. The explanation is on page 222 of AoPS Intro to Alg. I am guessing it's undefined because the next question in the Dolciani book is the same but this time, gives slope = 0.

[quark]

what's "no slope"?  is the slope zero (y=0) or is the slope undefined (x=0) ?  If this is a problem in aops, please post the number so I can look at their solution :).  

 

But yes, I'd be irked if I had to show work for that too, though it can be done, just a lot of zeros involved... ( y = 0(x) + 0 ?)

 

 

I went from y = mx + c (slope intercept form) to Ax + By = C (standard form)

c = 0 (pass through origin)

m = 0 (no slope)

y = 0

0x + y = 0

Think I need another round of coffee.

 

Exactly! The 0's for x and y and then assuming m here is undefined as well... :leaving:

[quark]

OK, the textbook itself doesn't really ask to show work. I am using a sentence format/ paragraph format for explaining my answer very similar to what AoPS is using on that page 222 but am wondering if there's a better way.

[Dana]

I tell my students that "no slope" is nonsense, so that phrasing really irks me. You can have slope of zero or undefined slope. "No slope" is unclear.

 

I don't have the AoPS algebra text, but depending on where you are in explanations at this point, I'd say an undefined slope is a vertical line, so the equation has to be x= #. You're going through the origin, so x=0.

[regentrude]

If "no slope" means "zero slope", the line would be y=0:

 

y=mx+c

m=0

must go through origin, so y-intercept is c=0

y=0

 

If "no slope" means slope goes to undefined, the line would be x=0. (I would consider the problem poorly worded.).

m=(y2-y1)/(x2-x1) is undefined if denominator is zero, i.e. x2=x1. Since x=0 must be included,  x=0 is the equation.

 

I find the only sensible interpretation of "no slope" to mean "zero slope", since we use the word "no" to mean "zero" in other connotations as well.

[kiana]

No slope is a very confusing way to phrase it. I wouldn't know myself what they meant without checking the answer manual.

[quark]

Thanks everyone...I'm relieved that I'm not the only one who has an issue with the terminology. Thankfully DS is okay with the book (his tutor recommends Dolciani) because we use multiple resources anyway and he usually prefers undefined vs. no slope. I'm trying to work ahead of him whenever I have time (which isn't often enough).

 

I tell my students that "no slope" is nonsense, so that phrasing really irks me. You can have slope of zero or undefined slope. "No slope" is unclear.

I don't have the AoPS algebra text, but depending on where you are in explanations at this point, I'd say an undefined slope is a vertical line, so the equation has to be x= #. You're going through the origin, so x=0.

 

Bolded is similar to my answer to the problem. Thanks Dana! I was wondering how to show it using the m=(y2-y1)/(x2-x1) method...regentrude has helpfully outlined that below so I will keep studying it and ask again if I am stumped.

 

If "no slope" means "zero slope", the line would be y=0:

 

y=mx+c

m=0

must go through origin, so y-intercept is c=0

y=0

 

If "no slope" means slope goes to undefined, the line would be x=0. (I would consider the problem poorly worded.).

m=(y2-y1)/(x2-x1) is undefined if denominator is zero, i.e. x2=x1. Since x=0 must be included,  x=0 is the equation.

 

I find the only sensible interpretation of "no slope" to mean "zero slope", since we use the word "no" to mean "zero" in other connotations as well.

 

I agree. But the textbook clearly means undefined when using "no slope". It clearly states slope = 0 for the horizontal line y=#. So glad we have AoPS and a few other resources on standby for moments like these.

 

Can anyone who has used Dolciani for Alg2+Trig comment on your experience?

[Kathy in Richmond]

I used Dolciani Alg 2 for my son & liked it, so i was curious to check this out & found your problem in section 3-4 of my 1992 copy.

 

I'd totally forgotten that Dolciani states 'vertical lines have no slope' in the previous section (3-3). I probably just told my son that it meant the slope was undefined (preferred terminology)

 

Here's how I would explain your problem (long-winded version :-))

 

In section 3-3, Dolciani gives the general form of the equation of the straight line as  Ax + By = C,

 

& states a theorem that  "the slope of the line Ax + By = C when B not equal to 0 is -A/B"

 

So, the only way that the slope could be undefined would be for B=0 and A not equal to 0.

 

The general form thus reduces to Ax = C. But the line passes through the origin, so A*0 = C, or C=0.

 

Now the general form reduces to Ax = 0.

 

We can divide both sides by A, since A not equal to 0, giving us the final answer x=0 for the line's equation.

[quark]

Thank you Kathy! I prefer the long winded version...I like to read it over and over again! :) I should have stated the section and page # to save you some trouble. Thanks again. I have the 1994 ed. ...not much is different from the 1992 ed., I believe.

 

OK quick question for anyone willing to answer it. Was "no slope" used prior to 2000 or something like that in US textbooks? I found a 1997 reference on Math Forum where undefined slope = no slope. This is another generally respected resource I like to consult when stumped.

[Kathy in Richmond]

Thank you Kathy! I prefer the long winded version...I like to read it over and over again! :) I should have stated the section and page # to save you some trouble. Thanks again. I have the 1994 ed. ...not much is different from the 1992 ed., I believe.

 

No problem! I enjoying looking through the books on my math shelves. It's my favorite way to procrastinate (especially when I should be paying the bills).

 

OK quick question for anyone willing to answer it. Was "no slope" used prior to 2000 or something like that in US textbooks? I found a 1997 reference on Math Forum where undefined slope = no slope. This is another generally respected resource I like to consult when stumped.

Hmmm... just checked a couple of old texts. My 1961 Dolciani alg 1 also uses "no slope," but another old algebra text from 1963 uses "undefined"