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If line k passes through the points (48, 33) and (31, 22)

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If line k passes through the points (48, 33) and (31, 22) [#permalink] New post 09 Jul 2018, 06:24
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Question Stats:

53% (02:35) correct 46% (01:29) wrong based on 28 sessions
If line k passes through the points (48, 33) and (31, 22), what is the x-intercept of line k?

A) -25 10/11
B) -3
C) -1 16/17
D) 1 16/17
E) 25 10/11

*I'll post a solution in 2 days
[Reveal] Spoiler: OA

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Re: If line k passes through the points (48, 33) and (31, 22) [#permalink] New post 10 Jul 2018, 19:45
We know that every single line in 2D has a formula: y=ax+b
This line goes through 2 points A(x1,y1),B(x2,y2) which means if we input x1 in the above formula we will have y1.
Then we have 2 equations for 2 unknowns a and b: 33=48a+b and 22=31a+b. Solve for a and b to have y=(11/17)*x+33/17
X-intercept means that the point intercept between the line and Ox which means y=0 then solve for x=-3
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Re: If line k passes through the points (48, 33) and (31, 22) [#permalink] New post 11 Jul 2018, 07:01
Expert's post
GreenlightTestPrep wrote:
If line k passes through the points (48, 33) and (31, 22), what is the x-intercept of line k?

A) -25 10/11
B) -3
C) -1 16/17
D) 1 16/17
E) 25 10/11


If we sketch the two given points, we can quickly see that the slope (aka rise/run) of the line = 11/17
Image

So, we can use this information to plot another point on the line...
Image

And another point...
Image
..at which point, we can see that the x-intercept is -3

Answer: B

Cheers,
Brent
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Re: If line k passes through the points (48, 33) and (31, 22) [#permalink] New post 18 Sep 2018, 13:18
i don't understand the solution for this one
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Re: If line k passes through the points (48, 33) and (31, 22) [#permalink] New post 19 Sep 2018, 03:15
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You can find the slope of the line k from the two given points.
slope = 11/17
now plug in the values of x=48 and y = 33 in the eqn y=mx +c
find the value of c which will be 33/17

Again plug in the value of y=0 in the eqn y = 11/17 * x + 33/17
solve for x and it will be -3
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Re: If line k passes through the points (48, 33) and (31, 22) [#permalink] New post 02 Nov 2018, 09:55
You need to keep all the solutions in fractions, getting to the answer is simple that way
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Re: If line k passes through the points (48, 33) and (31, 22) [#permalink] New post 20 May 2019, 08:30
I did the math correctly. But it took really few minutes as I had to find SLOPE->Y intercept->X intercept.
Can any one please give a shorter way to solve such problems ?
Thanks in advance .
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Re: If line k passes through the points (48, 33) and (31, 22) [#permalink] New post 20 May 2019, 10:11
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I believe what Brent explained above is the fastest way.

Regards
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Re: If line k passes through the points (48, 33) and (31, 22)   [#permalink] 20 May 2019, 10:11
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