In the XY-Plane , is the slope of the line k equal to 0 ?
(1) The X- intercept of k is 0
(2) The y-intercept of k is 0.
Logically, OA E makes sense.
However, I need to understand what's wrong with the algebraic method. Please don't reply with an intuitive answer. There is no doubt about OA.
A
Let the equation of line be y=mx+c
1) X intercept => 0=mx+c => x=-c/m; Now if the x-intercept =0; it means that m could be either infinity or a non-zero. I believe that "Infinity/Infinity" is undefined. Hence, m will not be equal to Zero. No. This doesn't make sense. What am I missing here?
2) Y intercept => y= c =0; therefore, y=mx; Not sufficient.
1 and 2) x intercept = 0 and y-intercept = 0=> c=0 and c/m=0 => m is not equal to zero.
It's crazy, but I am a bit lost....
Thoughts?
Need expert help - Slope of a line
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 405
- Joined: Thu Feb 10, 2011 1:44 am
- Thanked: 3 times
- Followed by:1 members
GMAT/MBA Expert
- Anurag@Gurome
- GMAT Instructor
- Posts: 3835
- Joined: Fri Apr 02, 2010 10:00 pm
- Location: Milpitas, CA
- Thanked: 1854 times
- Followed by:523 members
- GMAT Score:770
If we consider the equation of the line as y = mx + c,voodoo_child wrote:Hence, m will not be equal to Zero. No. This doesn't make sense. What am I missing here?
Then from statement 1, we can conclude either of the following,
- 1. c = 0 and m = anything
- Note that for c = 0, m can be equal to zero. Which is possible when the line is nothing but the X-axis.
Taking both statements together, c = 0 and -c/m = 0. As c = 0, -c/m is always equal to zero regardless of the value of m. Hence, m may or may not be equal to zero.
Hence, both statements together are also not sufficient.
The correct answer is E.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
-
- Master | Next Rank: 500 Posts
- Posts: 405
- Joined: Thu Feb 10, 2011 1:44 am
- Thanked: 3 times
- Followed by:1 members
Anurag,Anurag@Gurome wrote:
- Note that for c = 0, m can be equal to zero. Which is possible when the line is nothing but the X-axis.
thanks for your reply. However, we are given that x-intercept = 0 => c/m = 0. Therefore, if C = 0; how could m equal to 0? 0/0 is an indeterminate form. m CANNOT equal to zero.
X-axis doesn't have an x-intercept = 0. X-intercept on the x-axis could be anything from -infinity to +infinity.
Thoughts?
- GmatMathPro
- GMAT Instructor
- Posts: 349
- Joined: Wed Sep 28, 2011 3:38 pm
- Location: Austin, TX
- Thanked: 236 times
- Followed by:54 members
- GMAT Score:770
The case of m=0 makes nonsense of your equation (x=-c/m) because the very step of going from mx=-c to x=-c/m assumes that m is not equal to 0. That is, dividing both sides of an equation by a quantity is ONLY valid if that quantity is not equal to zero. So your formula for x-intercept, by the nature of its existence, is not equipped to deal with the case m=0 because it is only valid in cases where m is NOT equal to zero.voodoo_child wrote: 1) X intercept => 0=mx+c => x=-c/m; Now if the x-intercept =0; it means that m could be either infinity or a non-zero. I believe that "Infinity/Infinity" is undefined. Hence, m will not be equal to Zero. No. This doesn't make sense. What am I missing here?