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In the coordinate plane, Line J passes through the origin as well as

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Bunuel
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In the coordinate plane, Line J passes through the origin as well as [#permalink] New post   11 Oct 2015, 09:30
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In the coordinate plane, Line J passes through the origin as well as points (a, 2) and (8, a). Which of the following could be the slope of Line J?

A. 1/4
B. 1/2
C. 1
D. 2
E. 4
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Re: In the coordinate plane, Line J passes through the origin as well as [#permalink] New post   11 Oct 2015, 11:19
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Bunuel wrote:
In the coordinate plane, Line J passes through the origin as well as points (a, 2) and (8, a). Which of the following could be the slope of Line J?

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

Kudos for a correct solution.

UPDATE
Slope: \(\frac{0-2}{0-a}=2/a\) \(\frac{0-a}{0-8}\)=a/8
\(\frac{2}{a}=a/8\) a=4 -- > Slope=2/a=1/2 Answer (B)
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Re: In the coordinate plane, Line J passes through the origin as well as [#permalink] New post   11 Oct 2015, 11:05
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Here we know that one of the point is Origin (0,0) and the other two points are (a,2) and (8,a) respectively.
Hence if we calculate and equate the slopes we would get the value of a .
Thus ,

m = y2-y1/x2-x1 => a-0/8-0 = 2-0/a-0 which gives us a^2 = 16 . We know slope is +ve because the points lie in the Ist quadrant.
Hence , putting the value of a we would get the slope as m =1/2

The answer is 1/2
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Re: In the coordinate plane, Line J passes through the origin as well as [#permalink] New post   18 Oct 2015, 12:19
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Bunuel wrote:
In the coordinate plane, Line J passes through the origin as well as points (a, 2) and (8, a). Which of the following could be the slope of Line J?

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

Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION:

That Line J passes through the origin gives you a very helpful bit of information regarding point-slope form (y = mx + b). That tells you that when x = 0, y = 0, meaning that 0 = 0 + b...meaning that b also equals 0. That takes a variable away, allowing you to get to work on the two points knowing that the line has a constant slope, m:

For point (a, 2), that means that 2 = ma.

For point (8, a), that means that a = 8m.

This means that you can plug in a = 8m into the first equation, allowing you to solve for m (the slope):

2 = 8m^2

1/4 = m^2

m = 1/2 (or -1/2).
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Re: In the coordinate plane, Line J passes through the origin as well as [#permalink] New post   12 Oct 2015, 11:27
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Bunuel wrote:
In the coordinate plane, Line J passes through the origin as well as points (a, 2) and (8, a). Which of the following could be the slope of Line J?

A. 1/4
B. 1/2
C. 1
D. 2
E. 40

Kudos for a correct solution.


Equation of line passing through center is given by
y=mx----(i)
(i) also passes through (a, 2) and (8, a)
therefore 2=ma and a=8m
on solving we get m=1/2

Answer : B
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Re: In the coordinate plane, Line J passes through the origin as well as [#permalink] New post   11 Nov 2015, 17:46
Hi, Kindly let me know if this is a good approach.

Assume a value for 'a'

In this e.g.: (4,2) and (8,4)

Determine the slope as (4-2)/(8-4) = 1/2

Option B?
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Re: In the coordinate plane, Line J passes through the origin as well as [#permalink] New post   11 Nov 2015, 22:22
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marvas8581 wrote:
Hi, Kindly let me know if this is a good approach.

Assume a value for 'a'

In this e.g.: (4,2) and (8,4)

Determine the slope as (4-2)/(8-4) = 1/2

Option B?


The point to note here is that if you plugged -4 for a the slope would come up as -1/2. So, algebraic approach, in my opinion, is better for this question.
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Re: In the coordinate plane, Line J passes through the origin as well as [#permalink] New post   16 Jun 2017, 02:16
Bunuel wrote:
In the coordinate plane, Line J passes through the origin as well as points (a, 2) and (8, a). Which of the following could be the slope of Line J?

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

Kudos for a correct solution.


The fact the line J passes through the origin simply means that the y intercept of the equation of line j is 0- more simply, we can just work backwards and plug in values because the slope is the only component of the equation of line j

2= (something) x
2= 1/2 (4)

4-2 / 8-4 results in the slope so this slope is valid

Thus
"B"
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Re: In the coordinate plane, Line J passes through the origin as well as [#permalink] New post   11 Nov 2022, 03:23
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Re: In the coordinate plane, Line J passes through the origin as well as [#permalink]
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