y=mx (as passes through (0,0)
(a,b)
b=am -> m=b/a
thus line y=(b/a)x
b+ve?
a)slope<0 not sufficient. slope = b/a
b)a<b not sufficient
a&b) b/a<0 thus a and b are of different signs. a<b thus b is +ve and a -s -ve
IMO C
lines and slopes
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manpsingh87
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let equation of line be y=mx+cdivya23 wrote:in xy plane line k pass thru origin and thru (a,b) whr ab not equal = 0 is b +ve
slope of line k -ve
a< b
[spoiler]ans = both[/spoiler]
as line passes through origin therefore 0=0+c; hence c=0;
therefore equation of line is y=mx;
also as line passes through a,b; therefore b=am;
m=b/a;
1) slope is -ve; i.e. m=b/a is negative i.e. a and b are of opposite signs;
now m can be negative if b=+ve and a=-ve; or b=-ve or a=+ve;
hence 1) alone is insufficient.
2)a<b;
m=b/a; here also b can assume both positive and negative values hence 2) alone is also not sufficient to answer the question.
combining 1 and 2 we have;
m=-ve and a<b;
m=b/a; now if b=-ve; as a will have to be negative because a<b; which is not possible because this results in b/a to be positive i.e. slope is positive;
if b=+ve; then a must be negative, because slope m is negative,
hence b is positive and answer is C
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