GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Oct 2019, 09:24

### 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

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

# In the xy-plane, if line k passes through the points (3, -4) and (a,b)

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58422
In the xy-plane, if line k passes through the points (3, -4) and (a,b)  [#permalink]

### Show Tags

04 Sep 2019, 23:10
00:00

Difficulty:

25% (medium)

Question Stats:

77% (01:48) correct 23% (01:59) wrong based on 62 sessions

### HideShow timer Statistics

Competition Mode Question

In the xy-plane, if line k passes through the points (3, -4) and (a, b), where b = 4a - 16 and a > 3 what is the slope of k?

A. -4
B. -1/2
C. 0
D. 2
E. 4

_________________
Intern
Joined: 22 Feb 2014
Posts: 46
Re: In the xy-plane, if line k passes through the points (3, -4) and (a,b)  [#permalink]

### Show Tags

04 Sep 2019, 23:24
2
In the xy-plane, if line k passes through the points (3, -4) and (a, b), where b = 4a - 16 and a > 3 what is the slope of k?

A. -4
B. -1/2
C. 0
D. 2
E. 4

If A is 4 then b is 0, Point will be (4,0)
Now slope = (0+4)/(4-3) = 4
If A is 6 then b is 8, Point will be (6,8)
Now slope = (8+4)/(6-3) = 4

Sent from my SM-G935F using Tapatalk
Manager
Joined: 17 Jan 2019
Posts: 111
Re: In the xy-plane, if line k passes through the points (3, -4) and (a,b)  [#permalink]

### Show Tags

04 Sep 2019, 23:38
2
In the xy-plane, if line k passes through the points (3, -4) and (a, b), where b = 4a - 16 and a > 3 what is the slope of k?

if a=4 , b=0
if a=5, b=4

slope=$$\frac{-4-0}{3-4}=\frac{-4}{-1}=4$$
slope=$$\frac{-4-4}{3-5}=\frac{-8}{-2}=4$$
therefore, E
Senior Manager
Status: Whatever it takes!
Joined: 10 Oct 2018
Posts: 383
GPA: 4
Re: In the xy-plane, if line k passes through the points (3, -4) and (a,b)  [#permalink]

### Show Tags

05 Sep 2019, 00:11
1
In the xy-plane, if line k passes through the points (3, -4) and (a, b), where b = 4a - 16 and a > 3 what is the slope of k?

A. -4
B. -1/2
C. 0
D. 2
E. 4

points (3, -4) and (a, b) where b = 4a - 16 and a > 3

if a=4, b=0

Points would be (3, -4) and (4, 0)
Slope of line=$$\frac{y2-y1}{x2-x1}$$ =$$\frac{0+4}{4-3}$$ = 4........option E

P.S: take any value of a (a>3), you'll get same slope.
_________________

ALL ABOUT GMAT- $$https://exampal.com/gmat/blog/gmat-score-explained$$
Senior Manager
Joined: 18 May 2019
Posts: 372
Re: In the xy-plane, if line k passes through the points (3, -4) and (a,b)  [#permalink]

### Show Tags

05 Sep 2019, 00:21
The generic equation of a line is y=mx+c
From the question stem, we know that a>3
Hence the slope cannot be negative and it cannot be 0 either.
Testing with m=2
y=2x+c
Plugging in (3,-4)
-4=2*3+c hence c= -10
y=2x-10
The x intercept has to be more than 3 if the equation of the line is correct
0=2x-10 meaning x=5.
Hence the slope is 2.

Posted from my mobile device
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5032
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: In the xy-plane, if line k passes through the points (3, -4) and (a,b)  [#permalink]

### Show Tags

05 Sep 2019, 01:12
for (a,b) b = 4a - 16 and a > 3
a=4 , b=0
m=y2-y1/x2-x1 ; -4/-1 ; 4
IMO E ; 4

In the xy-plane, if line k passes through the points (3, -4) and (a, b), where b = 4a - 16 and a > 3 what is the slope of k?

A. -4
B. -1/2
C. 0
D. 2
E. 4
Director
Joined: 24 Nov 2016
Posts: 636
Location: United States
Re: In the xy-plane, if line k passes through the points (3, -4) and (a,b)  [#permalink]

### Show Tags

05 Sep 2019, 04:12
Quote:
In the xy-plane, if line k passes through the points (3, -4) and (a, b), where b = 4a - 16 and a > 3 what is the slope of k?

A. -4
B. -1/2
C. 0
D. 2
E. 4

$$points(x,y): (3,-4);(a,4a-16)$$
$$slope(m)=\frac{y2-y1}{x2-x1}=\frac{4a-16-(-4)}{a-3}=\frac{4a-12}{a-3}=\frac{(a-3)+3a-9}{a-3}=\frac{(a-3)+3(a-3)}{a-3}=\frac{(a-3)(1+3)}{a-3}=4$$

Senior Manager
Joined: 07 Mar 2019
Posts: 331
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: In the xy-plane, if line k passes through the points (3, -4) and (a,b)  [#permalink]

### Show Tags

05 Sep 2019, 09:57
Let the eqn. of line k
y = mx + c with slope m.

Since the line k passes through (3, -4) and (a, b) both, we have equations
- 4 = m * 3 + c and b = m * a + c

Subtracting 2nd from 1st gives
- 4 - b = 3m – am
m = (4+b) / (a – 3)

From question b = 4a – 16 and a > 3

If a = 4 then b = 0
 m = 4 + 0 / (4 - 3)
 m = 4

_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
Senior Manager
Joined: 29 Jun 2019
Posts: 425
Re: In the xy-plane, if line k passes through the points (3, -4) and (a,b)  [#permalink]

### Show Tags

05 Sep 2019, 11:26
b-(-4)/a-3 = 4a-16+4/a-3=
4a-12/a-3
As a>3 so, A,B, and C could not be the answer. If we let a, 4 therefore b is 0.(4,0)
0-(-4)/4-3=4/1=4
Option E

Posted from my mobile device
_________________
Always waiting
Manager
Joined: 17 Jul 2014
Posts: 151
Re: In the xy-plane, if line k passes through the points (3, -4) and (a,b)  [#permalink]

### Show Tags

05 Sep 2019, 15:15
In the xy-plane, if line k passes through the points (3, -4) and (a, b), where b = 4a - 16 and a > 3 what is the slope of k?

Slope = $$\frac{b-(-4)}{a-3}$$
Let's say a = 4
b = 16-16 = 0
slope = $$\frac{0+4}{4-3}$$ = 4

Re: In the xy-plane, if line k passes through the points (3, -4) and (a,b)   [#permalink] 05 Sep 2019, 15:15
Display posts from previous: Sort by