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# If line k in the xy-coordinate plane has the equation Ax + By = C, wha

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Math Expert
Joined: 02 Sep 2009
Posts: 50627
If line k in the xy-coordinate plane has the equation Ax + By = C, wha  [#permalink]

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23 Jul 2018, 02:15
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15% (low)

Question Stats:

83% (00:43) correct 17% (00:27) wrong based on 70 sessions

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If line k in the xy-coordinate plane has the equation Ax + By = C, what is the slope of line k ?

(1) A = 2B

(2) C = 4B

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Posts: 7036
Re: If line k in the xy-coordinate plane has the equation Ax + By = C, wha  [#permalink]

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23 Jul 2018, 05:52
If line k in the xy-coordinate plane has the equation Ax + By = C, what is the slope of line k ?

(1) A = 2B
$$Ax+By=C..........2Bx+By=C.........2x+y=\frac{C}{B}........y=-2x+\frac{C}{B}$$...
Now this is in the form y=mx+C, where m is slope..
So slope =-2
Sufficient

(2) C = 4B
Ax+By=C..........Ax+By=4B......y=-(A/B)X+4
So slope is -(A/B)....we don't know values of A and B..
Insufficient

A
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Re: If line k in the xy-coordinate plane has the equation Ax + By = C, wha  [#permalink]

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23 Jul 2018, 06:42
I would first write the equation in the form of y = slope (x) + y-intercept and then check if the statements help.

Ax + By = C
By = -Ax + C
y = -(A/B)x + C/B

Slope = -A/B

1) If A = 2B then I'll be able to replace A and then cancel out the B's, thus sufficient.

2) C = 4B. With this information, I would be able to find the value of C/B but not of A/B so it's not sufficient.

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If line k in the xy-coordinate plane has the equation Ax + By = C, wha  [#permalink]

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23 Jul 2018, 08:37
Bunuel wrote:
If line k in the xy-coordinate plane has the equation Ax + By = C, what is the slope of line k ?

(1) A = 2B

(2) C = 4B

Given equation of line: Ax+By = C. We can simplify this equation further, as we know that the line of equation is in the form :
y = mx + c

Dividing the giving equation with coefficient of y to get the standard form:
(A/B)x + y = C/B or: y = -(A/B)x + C/B

In order to get the slope (m), we need the values of A/B.

(A) is sufficient to provide the slope of the line.
Given A = 2B
Hence, m = -(2B/B) = -2 SUFFICIENT

(B) By looking this option, it's not giving the relation between A and B. Also, after putting the value of C in equation, we will get the values in the form of A and B.
Hence, NOT SUFFICIENT

Therefore, Answer to this question is option A
CEO
Joined: 11 Sep 2015
Posts: 3122
Re: If line k in the xy-coordinate plane has the equation Ax + By = C, wha  [#permalink]

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15 Nov 2018, 07:23
Top Contributor
Bunuel wrote:
If line k in the xy-coordinate plane has the equation Ax + By = C, what is the slope of line k ?

(1) A = 2B

(2) C = 4B

Given: Line k has the equation Ax + By = C

Target question: What is the slope of line k ?
This is a good candidate for rephrasing the target question.
Let's take the given equation Ax + By = C and rewrite it in slope y-intercept form, y = mx + b, where m = slope and b = y-intercept

GIVEN: Ax + By = C
Subtract Ax from both sides to get: By = -Ax + C
Divide both sides by B to get: y = -Ax/B + C/B
Rewrite to get: y = (-A/B)x + C/B
With the line's equation written in this form, we can see that line k has slope -A/B and y-intercept C/B
So, we can REPHRASE our target question....
REPHRASED target question: What is the value of -A/B ?

Aside: Below is a video with tips on rephrasing the target question

Statement 1: A = 2B
Divide both sides by B to get: A/B = 2
This means -A/B = -2
So, the answer to the REPHRASED target question is -A/B = -2
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: C = 4B
Since we have no information about A, there's no way to determine the value of -A/B
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

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Re: If line k in the xy-coordinate plane has the equation Ax + By = C, wha &nbs [#permalink] 15 Nov 2018, 07:23
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