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

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Bunuel
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In the coordinate plane, Line M travels through points (9,10), (0,4), [#permalink] New post   29 May 2018, 22:34
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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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D
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Re: In the coordinate plane, Line M travels through points (9,10), (0,4), [#permalink] New post   29 May 2018, 22:57
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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 \(y=\frac{2}{3}x+4\).
\(n=\frac{2}{3}*(-9)+4=-2\)

Answer: D
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Re: In the coordinate plane, Line M travels through points (9,10), (0,4), [#permalink] New post   29 May 2018, 23:27
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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.

Answer: D
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In the coordinate plane, Line M travels through points (9,10), (0,4), [#permalink] New post   31 May 2018, 14:16
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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 \(=n\)
\(y=((\frac{2}{3}*-9)+4)=(-6+4)=-2=n\)

\(n = -2\)

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

Answer: D
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Re: In the coordinate plane, Line M travels through points (9,10), (0,4), [#permalink] New post   01 Sep 2021, 09:43
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Re: In the coordinate plane, Line M travels through points (9,10), (0,4), [#permalink]
01 Sep 2021, 09:43
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