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

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