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

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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

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VP  D
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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]

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

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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)
$$y=3x+3$$
$$21=3n+3$$
$$18=3n$$
$$n=6$$

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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 2942
Re: In the xy-coordinate system, points (2, 9) and (-1, 0) lie on line k.  [#permalink]

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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.

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Veritas Prep GMAT Instructor D
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]

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