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what is the y-intercept of line

Expert replies
Source: — Data Sufficiency |

by pbanavara » Mon Dec 08, 2008 7:00 pm
This has been answered before - please search for the question.

- pradeep
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Re: what is the y-intercept of line

by lunarpower » Tue Dec 09, 2008 5:09 am
(1)
y = mx + b

substitute m = 3b --> y = 3bx + b
this won't help us find b, so, insufficient.

(2)
graphically, we can draw a line through (-1/3, 0) with absolutely any slope we want. each of those lines will have a different y-intercept (with the exception of the one purely vertical line, which won't have a y-intercept at all).
insufficient.

(together)
substitute (-1/3, 0) into y = 3bx + b
0 = -b + b
0 = 0

this is a tautology, meaning that there is no further information to be learned from combining the two statements. in other words, the two statements are equivalent to one another.
for further proof of that equivalence, let's plug in the x-intercept of (-1/3, 0) only:
y = mx + b
0 = m(-1/3) + b
0 = (-1/3)m + b
(1/3)m = b
m = 3b
the slope is 3 times the y-intercept.
statement (2) is therefore equivalent to statement (1). since the individual statements are each insufficient, their "combination" (which really isn't much of a combination at all, because they're equivalent to each other) is still insufficient.

answer = (e).
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