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# A line that passes through (–1, –4) and (3, k) has a slope =

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Magoosh GMAT Instructor
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A line that passes through (–1, –4) and (3, k) has a slope = [#permalink]

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19 Nov 2012, 16:30
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A line that passes through (–1, –4) and (3, k) has a slope = k. What is the value of k?
(A) 3/4
(B) 1
(C) 4/3
(D) 2
(E) 7/2

See a full discussion of lines & slope in the x-y plane here:
http://magoosh.com/gmat/2012/gmat-math- ... x-y-plane/

Experts: feel free to add any other x-y plane advice you would like to share.
[Reveal] Spoiler: OA

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Re: A line that passes through (–1, –4) and (3, k) has a slope = [#permalink]

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29 Nov 2012, 10:32
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y=mx+c is the equation. Since the line passes through (-1,-4) and (3,k) substitute this for the value of x and y.

we get 2 equations

-4=-k+c...(1)
c=-2k.......(2)

Substitute for C in equation 1. we get k=4/3.

The ans is C.
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Re: A line that passes through (–1, –4) and (3, k) has a slope = k. What [#permalink]

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04 Mar 2015, 09:50
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(k+4)/(3+1)=(k+4)/4 this is the slope of the line

we also know that slope=k, then respectively

k=(k+4)/4
4k=k+4
k=4/3

Answ C
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Re: A line that passes through (–1, –4) and (3, k) has a slope = k. What [#permalink]

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04 Mar 2015, 11:57
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Since 2 points are given and we are told that a line passes through points (-1, -4) & ( 3,k) , so we have simple formula to line's slope.

slope = ( y2- y1)/ (x2-x1) Or : ( k-(-4) ) / ( 3-(-1)) = k+4/ 4 and we are told that this is equal to k

so we have : k+4/4 =k and multiple both sides by 4 and get : k+4 = 4k or 3 k=4 so , k= 4/3 answer c...
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Re: line with variable slope [#permalink]

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19 Nov 2012, 17:35
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mikemcgarry wrote:
A line that passes through (–1, –4) and (3, k) has a slope = k. What is the value of k?
(A) 3/4
(B) 1
(C) 4/3
(D) 2
(E) 7/2

See a full discussion of lines & slope in the x-y plane here:
http://magoosh.com/gmat/2012/gmat-math- ... x-y-plane/

Experts: feel free to add any other x-y plane advice you would like to share.

Slope = (y2-y1)/(x2-x1)
=> k = (k+4)/(3+1)
=> 4k = k+4
=> k =4/3

Ans C it is!
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Re: A line that passes through (–1, –4) and (3, k) has a slope = [#permalink]

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07 Dec 2012, 03:43
A line that passes through (–1, –4) and (3, k) has a slope = k. What is the value of k?

m = $$\frac{y2-y1}{x2-x1}$$
m = $$\frac{k-(-4)}{3-(-1)}$$

m = $$\frac{k+4}{4}$$ & $$m = k$$

$$k = \frac{k+4}{4}$$
$$4k = k+4$$
$$k = 4/3$$

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A line that passes through (–1, –4) and (3, k) has a slope = k. What [#permalink]

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04 Mar 2015, 03:10
Expert's post
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A line that passes through (–1, –4) and (3, k) has a slope = k. What is the value of k?

A. 3/4
B. 1
C. 4/3
D. 2
E. 7/2

Kudos for a correct solution.
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Kudos [?]: 93222 [0], given: 10553

Re: A line that passes through (–1, –4) and (3, k) has a slope = k. What [#permalink]

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08 Mar 2015, 13:13
Bunuel wrote:
A line that passes through (–1, –4) and (3, k) has a slope = k. What is the value of k?

A. 3/4
B. 1
C. 4/3
D. 2
E. 7/2

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

This is a considerably more difficult one, which will involve some algebra. Let’s say that the “first” point is (–1, –4) and the “second,” (3, k). The rise = k + 4, which involves a variable. The run = 3 – (–1) = 4. There the slope is (k + 4)/4, and we can set this equal to k and solve for k.
(k + 4)/4 = k
k + 4 = 4k
4 = 3k
k = 4/3

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Re: A line that passes through (–1, –4) and (3, k) has a slope = k. What [#permalink]

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14 Jul 2016, 03:47
Slope = Delta y/Delta x
$$k=\frac{k-(-4)}{3-(-1)} ===>k= \frac{k+4}{4} ===>4k=k+4 ==>3k=4$$therefore $$k=\frac{4}{3}$$

Bunuel wrote:
A line that passes through (–1, –4) and (3, k) has a slope = k. What is the value of k?

A. 3/4
B. 1
C. 4/3
D. 2
E. 7/2

Kudos for a correct solution.

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Re: A line that passes through (–1, –4) and (3, k) has a slope = [#permalink]

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26 Aug 2016, 04:28
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Re: A line that passes through (–1, –4) and (3, k) has a slope =   [#permalink] 26 Aug 2016, 04:28
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