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Line interceptor

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by Leon1984 » Wed Oct 28, 2009 4:50 am
On the xy plane, what is the y intercept of line L?
(i) The slope of line L is 3 times the y intercept
(ii) The x intercept of line L is -1/3

I didn't even know how to approach this one. Please explain on the approach and the process of solving.

Thank you
Leon
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Source: — Data Sufficiency |
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by mp2437 » Wed Oct 28, 2009 6:20 am
Equation of line is y = mx + b, where m is slope and b = y-intercept.

(i) This is saying m = 3b, so the line becomes y = (3b)x + b. This is not sufficient by itself to solve for b since x and y are unknown.

(ii) x-intercept means the value of x when y is equal to 0.

Your equation becomes 0 = m(-1/3) + b, or m = 3b. Cannot solve for b by itself, so also insufficient.

Using (i + ii): They both give you the same info, m = 3b, but you cannot clearly solve for b, so it is insufficient.

Choice E.
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by Leon1984 » Wed Oct 28, 2009 7:55 am
Thank you. Should this be the general approach when dealing with this kind of questions?
Leon
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by mp2437 » Wed Oct 28, 2009 8:57 am
Generally, yes. My approach has always been to translate what's given, along with each statement, into an equation, and then see if either of them are sufficient to answer the question. If not, I look at the 2 equations from the statements together, and in cases where there are two equations and two unknowns, you know it can be solved, however, if the 2 statements yield the same equation, as is the case here, you cannot solve it.
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