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If the line passes through the origin, what is the value of k?

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Bunuel
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If the line passes through the origin, what is the value of k? [#permalink] New post   23 Aug 2018, 23:15
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If the line passes through the origin, what is the value of k?


A. -8
B. -12.5
C. -18
D. -24.5
E. -28

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D
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Re: If the line passes through the origin, what is the value of k? [#permalink] New post   24 Aug 2018, 00:16
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The slope of both points will be the same
k-0/14-0 = 7-0/-4-0
k = -24.5
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BrentGMATPrepNow
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Re: If the line passes through the origin, what is the value of k? [#permalink] New post   20 Feb 2020, 07:50
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Bunuel wrote:

If the line passes through the origin, what is the value of k?


A. -8
B. -12.5
C. -18
D. -24.5
E. -28
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Since the line passes through the origin, we know that the point (0, 0) also lies on the line.

Key property: The slope between any two points on a line will always be the same
This means: the slope between points (-4, 7) and (0, 0) must be equal to slope between points (0, 0) and (14, k)

We can now apply the slope formula to write: \(\frac{0 - 7}{0 - (-4)}=\frac{k - 0}{14 - 0}\)

Simplify: \(\frac{-7}{4}=\frac{k}{14}\)

Cross multiply to get: \(4k = (-7)(14)\)

Divide both sides of the equation by 4 to get: \(k = \frac{(-7)(14)}{4}= \frac{-98}{4}=-24.5\)

Answer: D

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Re: If the line passes through the origin, what is the value of k? [#permalink] New post   23 Aug 2018, 23:24
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Bunuel wrote:

If the line passes through the origin, what is the value of k?


A. -8
B. -12.5
C. -18
D. -24.5
E. -28

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Attachment:
GMAT_PS_Magoosh_85.png


Equation of line passing through the given points (-4,7) and (14,k) is:

\(y-7=\frac{k-7}{14-(-4)}*(x-(-4))\)

Since this line passes through origin(0,0), hence

\(0-7= \frac{k-7}{18}*(0+4)\)
Or, \(k-7=\frac{-7*18}{4}\)
Or, k=-31.5+7=-24.5

Ans. (D)
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Re: If the line passes through the origin, what is the value of k? [#permalink] New post   03 May 2021, 00:42
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\(\frac{K}{7} = \frac{14}{-4}\)

K = \(\frac{14 * 7}{ -4} = -24.5\)

Answer D
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Re: If the line passes through the origin, what is the value of k? [#permalink] New post   11 Sep 2023, 12:14
If the line passes through the origin, what is the value of k?

When a line passes through the origin, its equation becomes y=mx where m is the slope of the line

For 1st point
=>7=-4m i.e. => m = -7/4
For 2nd pint
=> k=14m =14*-7/4 = -24.5

Hence D
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Re: If the line passes through the origin, what is the value of k? [#permalink]
11 Sep 2023, 12:14
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