DS: In the xy-plane, what is the y-intercept of line l?

[NAS]

In the xy-plane, what is the y-intercept of line l?
1. The slope of the line l is 3 times its y-intercept
2. The x-intercept of line l is -1/3

Can someone explain the approach to solve this? Thanks. (OA is E)

[kylo]

equation of a line is given by -
Ax + By + C = 0 where C is a constant.

slope = -A/B
X-intercept = -C/A
Y-intercept = -C/B


from stat1 --> -A/B = 3*(-C/B)
solving we get -C/A = -1/3 or X-intercept = -1/3. hence insufficient.

from stat2 we get the same data as that given by stat1.


hence IMO E.


Thanks!

[RonPurewal]

(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 (= equation that's always true), so it provides no information about variables. put another way, it will be true regardless of the value of b (try substituting in a few values yourself if you don't see why).
insufficient.

answer = (e).