In the xy-plane, what is the y-intercept

[dtriffonov]

In the xy-plane, what is the y-intercept of line L?

(1) The slope of line L is 3 times its y-intercept?
(2) The x-intercept of line L is (-1/3)

walk me through the solution please. Thanks,
Daniel

[nitin_prakash_khanna]

let the line be
y = mx+c

whats the y intercept, i.e when x = 0 , y=c
So question is asking what's c?

St 1 -> Slope which m = 3 c.
Doesnt help so insufficient.

St 2 -> x intercept which when y = 0, x = -c / m = -1/3
which gives m = 3c
not much help. so insufficient.

Combine both all we get is m= 3c
Nothing new.

So Ans E.
Hope its the OA

[dtriffonov]

thank you.

[RonPurewal]

(1)
y = mx + b

substitute m = 3b --> y = 3bx + b
you can factor out b to give y = (3x + 1)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
so, nothing new here. this is a tautology (i.e., it's always true), so we haven't found out anything new.
so still insufficient.

ans (e)

[dtriffonov]

thanks Ron.

[RonPurewal]

thanks Ron.

sweetness

[benkriger]

I got tricked on my last test in this when i arrived at 0=0. I said "ah hah, always true, must be sufficient"... But in reality, this equation does not tell us anything to answer the question.

[tim]

yes, keep in mind there is always a question to answer! don't get distracted by intermediate results.. :)

[Karthik_murugiah]

In practice can someone tell me how to visualize the first point --> the slope of line L is 3 times its y-intercept

How can this be possible? for any line (which is not a parabola) the slope is constant while the x and y intercepts change. How can a line segment in space be constructed with this data?

[RonPurewal]

How can this be possible? for any line (which is not a parabola) the slope is constant while the x and y intercepts change.

i think i see the problem here: it appears that you're confusing the notion of xy-coordinates, in general, with the much more specific idea of x- and y-intercepts.

coordinates are, indeed, things that change as you move through the different points on a line.
on the other hand, the x-intercept is the single x-coordinate at which a line hits the x-axis, and the y-intercept is the single y-coordinate at which a line hits the y-axis. these two are constants, just as the slope of a line is a constant.

--

as for visualizing the comparison, there's no really straightforward way to do that, because an intercept (which is the location of a coordinate) isn't directly comparable to a slope value. so, this is one of the minority of problems on which you basically just have to sock it out with algebra.

(as an analogy, if i tell you that my body weight, in pounds, is 2.5 times my height in inches, that's a purely mathematical statement; a weight and a height are not actually comparable notions, so you can't really visualize that relationship. instead, you just have to think about different combinations of numbers that satisfy it -- like, say, a height of 6 feet [= 72 inches] and a body weight of 180 pounds -- and then picturing what such a person would look like.)

[abdul_tt]

Hi Ron,

Thanks for such beautiful analogies and awesome explanations. Manhattan instructors explanations are just brilliant , but Ron's are simply out of this world. what amuses me is the consistency of these explanations; That is I never found an incomplete or haphazard explanations by Manhattan Team till date.

[jlucero]

Glad to hear we're appreciated.

[tim]

glad to hear our consistency amuses you.. :)