Vincen wrote: ↑Fri Jun 19, 2020 2:41 am
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) \(C = 4B\)
[spoiler]OA=A[/spoiler]
Source: Magoosh
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
Answer: A
