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# In the coordinate plane, Line M travels through points (9,10), (0,4),

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Joined: 02 Sep 2009
Posts: 46302
In the coordinate plane, Line M travels through points (9,10), (0,4), [#permalink]

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29 May 2018, 22:34
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Difficulty:

25% (medium)

Question Stats:

84% (01:03) correct 16% (01:01) wrong based on 57 sessions

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In the coordinate plane, Line M travels through points (9,10), (0,4), and (−9,n). What is the value of n?

A. −10

B. −6

C. −10/3

D. −2

E. −4/3

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Re: In the coordinate plane, Line M travels through points (9,10), (0,4), [#permalink]

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29 May 2018, 22:57
1
Bunuel wrote:
In the coordinate plane, Line M travels through points (9,10), (0,4), and (−9,n). What is the value of n?

A. −10

B. −6

C. −10/3

D. −2

E. −4/3

Line $$M$$ can be expressed as
$$y=kx+b$$

We have the system of equations
$$9k+b=10$$
$$0+b=4$$

So, $$b=4$$, $$k=\frac{2}{3}$$ and $$y=\frac{2}{3}x+4$$

Now, let's check $$(−9,n)$$ with $$y=\frac{2}{3}x+4$$.
$$n=\frac{2}{3}*(-9)+4=-2$$

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Re: In the coordinate plane, Line M travels through points (9,10), (0,4), [#permalink]

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29 May 2018, 23:27
2
1

Solution

Given:
• In the coordinate plane, Line M travels through points (9, 10), (0, 4), and (-9, n)

To find:
• The value of n

Approach and Working:
As the points are colinear, the slope calculated by taking any points at a time will be the same always.
Therefore, we can write
• $$\frac{(4-10)}{(0-9)} = \frac{(n-4)}{(-9-0)}$$
Or, $$\frac{-6}{-9} = \frac{(n – 4)}{-9}$$
Or, n = -2

Hence, the correct answer is option D.

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In the coordinate plane, Line M travels through points (9,10), (0,4), [#permalink]

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31 May 2018, 14:16
Bunuel wrote:
In the coordinate plane, Line M travels through points (9,10), (0,4), and (−9,n). What is the value of n?

A. −10

B. −6

C. −10/3

D. −2

E. −4/3

We need an equation for the line.
Any point on the line makes the equation true.
We have point (-9,n). x-coordinate is -9.
Plug -9 into line's equation. Result is the y-coordinate for that point, here called $$n$$.

Slope intercept form is easy to use, thus:
$$y=mx+b$$ in which $$m$$ = slope and $$b$$ = y-intercept

y-intercept: When $$x=0$$, $$y=?$$
From (0,4), y-intercept = $$+ 4 = b$$
So far we have: $$y=mx+4$$

Use given points (9,10) and (0,4). Find slope

Slope = $$m$$
Slope=$$\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{10-4}{9-0}=\frac{6}{9}=\frac{2}{3}=m$$

Equation of the line
We have: $$y=\frac{2}{3}x+4$$

Coordinates
$$(-9,n)$$: what is $$n$$?
Plug $$x=-9$$ into equation
For THIS point, y-coordinate $$=n$$
$$y=((\frac{2}{3}*-9)+4)=(-6+4)=-2=n$$

$$n = -2$$

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Re: In the coordinate plane, Line M travels through points (9,10), (0,4), [#permalink]

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31 May 2018, 16:15
Bunuel wrote:
In the coordinate plane, Line M travels through points (9,10), (0,4), and (−9,n). What is the value of n?

A. −10

B. −6

C. −10/3

D. −2

E. −4/3

Since line M travels though all the given points, the slopes between any pairs of points have to be the same; thus:

(4 - 10)/(0 - 9) = (n - 4)/(-9 - 0)

-6/-9 = (n - 4)/-9

-6 = n - 4

-2 = n

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Re: In the coordinate plane, Line M travels through points (9,10), (0,4),   [#permalink] 31 May 2018, 16:15
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