Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 18 Jul 2019, 02:05

### 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-coordinate system, points (2, 9) and (-1, 0) lie on line k.

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 56261
In the xy-coordinate system, points (2, 9) and (-1, 0) lie on line k.  [#permalink]

### Show Tags

23 Aug 2018, 04:59
00:00

Difficulty:

15% (low)

Question Stats:

86% (01:40) correct 14% (02:21) wrong based on 57 sessions

### HideShow timer Statistics

In the xy-coordinate system, points (2, 9) and (-1, 0) lie on line k. If the point (n, 21) lies on line k, what is the value of n?

A. 6
B. 7
C. 8
D. 9
E. 10

_________________
VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1028
WE: Supply Chain Management (Energy and Utilities)
Re: In the xy-coordinate system, points (2, 9) and (-1, 0) lie on line k.  [#permalink]

### Show Tags

23 Aug 2018, 05:06
1
Bunuel wrote:
In the xy-coordinate system, points (2, 9) and (-1, 0) lie on line k. If the point (n, 21) lies on line k, what is the value of n?

A. 6
B. 7
C. 8
D. 9
E. 10

Equation of the line passing through points (2, 9) and (-1, 0):

$$y-9=\frac{0-9}{-1-2}*(x-2)$$
Or, y-9=3(x-2), this is the equation of the line k

If the point (n, 21) lies on line k, then this point must satisfy the above equation.
So, 21-9=3n-6
or, 3n-6=12
or, 3n=18
or, n=6

Ans. (A)
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
Senior SC Moderator
Joined: 22 May 2016
Posts: 3076
In the xy-coordinate system, points (2, 9) and (-1, 0) lie on line k.  [#permalink]

### Show Tags

23 Aug 2018, 20:13
Bunuel wrote:
In the xy-coordinate system, points (2, 9) and (-1, 0) lie on line k. If the point (n, 21) lies on line k, what is the value of n?

A. 6
B. 7
C. 8
D. 9
E. 10

Slope-intercept approach: Find the equation of line $$k$$ in slope-intercept form
$$y=mx+b$$
$$m$$ = slope
$$b$$ = y-intercept

1) Find slope. Use the coordinates of the two given points, (2,9) and (-1,0)

Slope: $$\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{0-9}{-1-2}=\frac{-9}{-3}=3$$

Plug slope into equation: $$y=3x+b$$

2) Find $$b$$. Plug (x,y) of either given point into equation. Example (-1,0):
$$y=3x+b$$
$$0=3(-1)+b$$
$$0=-3+b$$
$$b=3$$
Plug value of $$b$$ into equation

3) Full equation of line $$k$$ is $$y=3x+3$$. Every point (x, y) [and (n, 21)] on a line must satisfy the equation of the line.

4) Point (n, 21) lies on line $$k$$
$$n =?$$ (n = x-coordinate). Plug in (n, 21)
$$y=3x+3$$
$$21=3n+3$$
$$18=3n$$
$$n=6$$

_________________
SC Butler has resumed!
Get two SC questions to practice, whose links you can find by date, here.

Tell me, what is it you plan to do with your one wild and precious life? -- Mary Oliver
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2942
Re: In the xy-coordinate system, points (2, 9) and (-1, 0) lie on line k.  [#permalink]

### Show Tags

23 Aug 2018, 22:00

Solution

Given:
• Points (2, 9) and (-1, 0) lie on line k

To find:
• The value of n such that point (n, 21) also lies on line k.

Approach and Working:

• Points (2, 9) and (-1, 0) lie on line k.
o Hence, slope of line k=$$\frac{{9-0}}{{2- (-1)}}$$= $$\frac{9}{3}$$= 3

• Now, if point (n, 21) also lies on line k then the slope of (n, 21) and(-1, 0) will also be equal to 3.
o $$\frac{{21-0}}{{n+1}}$$= 3
o n=6

Hence, the correct answer is option A.

_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9442
Location: Pune, India
Re: In the xy-coordinate system, points (2, 9) and (-1, 0) lie on line k.  [#permalink]

### Show Tags

23 Aug 2018, 22:06
Bunuel wrote:
In the xy-coordinate system, points (2, 9) and (-1, 0) lie on line k. If the point (n, 21) lies on line k, what is the value of n?

A. 6
B. 7
C. 8
D. 9
E. 10

Simply use the concept of slope (which many of us think of as Rise/Run) - It is the change in y co-ordinate for a unit change in x co-ordinate)
(2, 9), (-1 , 0) - When x co-ordinate reduces by 3 units, y co-ordinate reduces by 9 units (3 times).
(-1, 0), (n, 21) - So when y co-ordinate increase by 21 units, x co-ordinate will increase by 7 units (1/3).
So n = 6

For more, check: https://www.veritasprep.com/blog/2016/0 ... line-gmat/
_________________
Karishma
Veritas Prep GMAT Instructor

Re: In the xy-coordinate system, points (2, 9) and (-1, 0) lie on line k.   [#permalink] 23 Aug 2018, 22:06
Display posts from previous: Sort by