NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 00:15 It is currently 24 Apr 2024, 00:15
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If line k in the xy-plane has equation y = mx + b, where m and b are

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
udaymathapati
Manager
Manager
Joined: 06 Apr 2010
Posts: 93
Own Kudos [?]: 4922 [107]
Given Kudos: 15
Send PM
Reviews Badge
If line k in the xy-plane has equation y = mx + b, where m and b are [#permalink] New post   02 Sep 2010, 12:52
5
Kudos
100
Bookmarks
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

65% (01:53) correct 35% (02:06) wrong based on 2126 sessions
Hide Show timer Statistics
If line k in the xy-plane has equation y = mx + b, where m and b are constants, what is the slope of k?


(1) k is parallel to the line with equation \(y = (1-m)x + b +1\).

(2) k intersects the line with equation \(y = 2x + 3\) at the point (2, 7).
ShowHide Answer
Official Answer
A
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92888
Own Kudos [?]: 618657 [26]
Given Kudos: 81564
Send PM
CAT Tests Forum Quiz Mode
Re: If line k in the xy-plane has equation y = mx + b, where m and b are [#permalink] New post   02 Sep 2010, 13:19
13
Kudos
12
Bookmarks
Expert Reply
If Line k in the xy-plane has equation y = mx + b, where m and b are constants, what is the slope of k?

\(y=mx+b\) is called point-intercept form of equation of a line. Where: \(m\) is the slope of the line; \(b\) is the y-intercept of the line; \(x\) is the independent variable of the function \(y\).

So we are asked to find the value of \(m\).

(1) k is parallel to the line with equation y = (1-m)x + b +1 --> parallel lines have the same slope --> slope of this line is \(1-m\), so \(1-m=m\) --> \(m=\frac{1}{2}\). Sufficient.

(2) k intersects the line with equation y = 2x + 3 at the point (2, 7) --> so line k contains the point (2,7) --> \(7=2m+b\) --> can not solve for \(m\). Not sufficient.

Answer: A.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92888
Own Kudos [?]: 618657 [21]
Given Kudos: 81564
Send PM
CAT Tests Forum Quiz Mode
Re: If line k in the xy-plane has equation y = mx + b, where m and b are [#permalink] New post   26 Mar 2012, 14:15
4
Kudos
16
Bookmarks
Expert Reply
For Coordinate Geometry check:

24. Coordinate Geometry



For more check:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread

Hope it helps.
General Discussion
avatar
gnan
Intern
Intern
Joined: 26 May 2012
Status:ISB 14...:)
Posts: 19
Own Kudos [?]: 77 [0]
Given Kudos: 11
Location: India
Concentration: Strategy
Schools: ISB '14 (A)
GMAT 1: 750 Q51 V39
GPA: 3.62
WE:Engineering (Energy and Utilities)
Send PM
Reviews Badge
Re: If line k in the xy-plane has equation y = mx + b, where m and b are [#permalink] New post   07 Jun 2012, 00:54
For line K, y=mx+b implies slope=m

From Statement-1,

As slopes of parallel lines are equal, m = (1-m)

m=1/2
Statement-1 is sufficient.

From statement-2,

line K passes through (2,7)
7=2.m + b
m = (7-b)/2
Not sufficient.

Ans:A
User avatar
S
Gmatprep550
Manager
Manager
Joined: 21 Jul 2018
Posts: 149
Own Kudos [?]: 65 [0]
Given Kudos: 186
Send PM
Reviews Badge
Re: If line k in the xy-plane has equation y = mx + b, where m and b are [#permalink] New post   29 Mar 2019, 13:51
Hi chetan2u, VeritasKarishma, Bunuel, amanvermagmat, gmatbusters,

I did not understood the bold part in below question, can any please assist.

Bunuel wrote:
If Line k in the xy-plane has equation y = mx + b, where m and b are constants, what is the slope of k?

\(y=mx+b\) is called point-intercept form of equation of a line. Where: \(m\) is the slope of the line; \(b\) is the y-intercept of the line; \(x\) is the independent variable of the function \(y\).

So we are asked to find the value of \(m\).

(1) k is parallel to the line with equation y = (1-m)x + b +1 --> parallel lines have the same slope --> slope of this line is \(1-m\), so \(1-m=m\) --> \(m=\frac{1}{2}\). Sufficient.

(2) k intersects the line with equation y = 2x + 3 at the point (2, 7) --> so line k contains the point (2,7) --> \(7=2m+b\) --> can not solve for \(m\). Not sufficient.

Answer: A.
User avatar
L
GMATBusters
GMAT Tutor
Joined: 27 Oct 2017
Posts: 1907
Own Kudos [?]: 5579 [1]
Given Kudos: 236
WE:General Management (Education)
Send PM
GMAT ToolKit User
Re: If line k in the xy-plane has equation y = mx + b, where m and b are [#permalink] New post   29 Mar 2019, 23:05
1
Kudos
Expert Reply
Hi

I couldd not get your query, the principle is as below:



Show Spoiler
Attachment:
1.jpg
1.jpg [ 20.17 KiB | Viewed 32415 times ]

Show Spoiler
Attachment:
2.PNG
2.PNG [ 18.18 KiB | Viewed 32438 times ]


Gmatprep550 wrote:
Hi chetan2u, VeritasKarishma, Bunuel, amanvermagmat, gmatbusters,

I did not understood the bold part in below question, can any please assist.

Bunuel wrote:
If Line k in the xy-plane has equation y = mx + b, where m and b are constants, what is the slope of k?

\(y=mx+b\) is called point-intercept form of equation of a line. Where: \(m\) is the slope of the line; \(b\) is the y-intercept of the line; \(x\) is the independent variable of the function \(y\).

So we are asked to find the value of \(m\).

(1) k is parallel to the line with equation y = (1-m)x + b +1 --> parallel lines have the same slope --> slope of this line is \(1-m\), so \(1-m=m\) --> \(m=\frac{1}{2}\). Sufficient.

(2) k intersects the line with equation y = 2x + 3 at the point (2, 7) --> so line k contains the point (2,7) --> \(7=2m+b\) --> can not solve for \(m\). Not sufficient.

Answer: A.
User avatar
S
Gmatprep550
Manager
Manager
Joined: 21 Jul 2018
Posts: 149
Own Kudos [?]: 65 [0]
Given Kudos: 186
Send PM
Reviews Badge
Re: If line k in the xy-plane has equation y = mx + b, where m and b are [#permalink] New post   30 Mar 2019, 00:19
gmatbusters wrote:
Hi

I couldd not get your query, the principle is as below:



Show Spoiler
Attachment:
1.jpg

Show Spoiler
Attachment:
2.PNG


Gmatprep550 wrote:
Hi chetan2u, VeritasKarishma, Bunuel, amanvermagmat, gmatbusters,

I did not understood the bold part in below question, can any please assist.

Bunuel wrote:
If Line k in the xy-plane has equation y = mx + b, where m and b are constants, what is the slope of k?

\(y=mx+b\) is called point-intercept form of equation of a line. Where: \(m\) is the slope of the line; \(b\) is the y-intercept of the line; \(x\) is the independent variable of the function \(y\).

So we are asked to find the value of \(m\).

(1) k is parallel to the line with equation y = (1-m)x + b +1 --> parallel lines have the same slope --> slope of this line is \(1-m\), so \(1-m=m\) --> \(m=\frac{1}{2}\). Sufficient.

(2) k intersects the line with equation y = 2x + 3 at the point (2, 7) --> so line k contains the point (2,7) --> \(7=2m+b\) --> can not solve for \(m\). Not sufficient.

Answer: A.


Hi gmatbusters

Apologies for not highlighting proper issue,

I was not able to get following part.


slope of this line is 1−m1−m, so 1−m=m1−m=m

Even if slope is m then also how 1-m = m? I feel that "m" mentioned in equation is different.
avatar
B
arsalansyed21
Intern
Intern
Joined: 12 Jun 2019
Posts: 13
Own Kudos [?]: 6 [0]
Given Kudos: 26
GMAT 1: 560 Q38 V28
GMAT 2: 610 Q43 V30
Send PM
Re: If line k in the xy-plane has equation y = mx + b, where m and b are [#permalink] New post   29 Jul 2019, 22:11
Parallel lines have same slopes buddy

Posted from my mobile device
User avatar
L
dave13
VP
VP
Joined: 09 Mar 2016
Posts: 1160
Own Kudos [?]: 1017 [0]
Given Kudos: 3851
Send PM
If line k in the xy-plane has equation y = mx + b, where m and b are [#permalink] New post   24 Sep 2020, 04:52
Bunuel wrote:
If Line k in the xy-plane has equation y = mx + b, where m and b are constants, what is the slope of k?

\(y=mx+b\) is called point-intercept form of equation of a line. Where: \(m\) is the slope of the line; \(b\) is the y-intercept of the line; \(x\) is the independent variable of the function \(y\).

So we are asked to find the value of \(m\).

(1) k is parallel to the line with equation y = (1-m)x + b +1 --> parallel lines have the same slope --> slope of this line is \(1-m\), so \(1-m=m\) --> \(m=\frac{1}{2}\). Sufficient.

(2) k intersects the line with equation y = 2x + 3 at the point (2, 7) --> so line k contains the point (2,7) --> \(7=2m+b\) --> can not solve for \(m\). Not sufficient.

Answer: A.



HiBunuel

for st 1 after equating equations i am getting 1 = 2mx-x

(1-m)x + b +1 = mx+b

or x-mx+b+1 = mx+b

1 = mx+b-x+mx-b

1= 2mx-x

what am i doing wrong :?
avatar
B
Mahi14
Intern
Intern
Joined: 03 Sep 2020
Posts: 4
Own Kudos [?]: 2 [2]
Given Kudos: 27
Send PM
Re: If line k in the xy-plane has equation y = mx + b, where m and b are [#permalink] New post   29 Sep 2020, 09:27
2
Kudos
For statement 2, can we use m1*m2 =-1 for intersecting lines?

Posted from my mobile device
avatar
B
adkor95
Intern
Intern
Joined: 06 Mar 2020
Posts: 34
Own Kudos [?]: 13 [0]
Given Kudos: 80
Send PM
Re: If line k in the xy-plane has equation y = mx + b, where m and b are [#permalink] New post   29 Oct 2020, 10:31
Bunuel wrote:
If Line k in the xy-plane has equation y = mx + b, where m and b are constants, what is the slope of k?

\(y=mx+b\) is called point-intercept form of equation of a line. Where: \(m\) is the slope of the line; \(b\) is the y-intercept of the line; \(x\) is the independent variable of the function \(y\).

So we are asked to find the value of \(m\).

(1) k is parallel to the line with equation y = (1-m)x + b +1 --> parallel lines have the same slope --> slope of this line is \(1-m\), so \(1-m=m\) --> \(m=\frac{1}{2}\). Sufficient.

(2) k intersects the line with equation y = 2x + 3 at the point (2, 7) --> so line k contains the point (2,7) --> \(7=2m+b\) --> can not solve for \(m\). Not sufficient.

Answer: A.


Thanks! But is this implying that no matter the format of the equation, the term/number multiplying the x-value is the gradient? I was thrown off by '+ 1' in the equation.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32636
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: If line k in the xy-plane has equation y = mx + b, where m and b are [#permalink] New post   27 Jan 2024, 10:01
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: If line k in the xy-plane has equation y = mx + b, where m and b are [#permalink]
27 Jan 2024, 10:01
Moderator:
Bunuel
Math Expert
92883 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions