yes, if you look at it from a purely 'equation of a line perspective' the point (4,3) info is not needed
product of slopes ( refer logitech's calculation) = b1b2/a1a2
to check if b1b2/a1a2 is < 0 we just need to know the signs of the numerator and the denominator and we are through!
Stmt 1 does just that but only provides sign of the denominator. so insufficient a1a2 >0
Stmt 2: provides sign of the numerator. numerator b1b2 < 0
only after combining the 2 statements can we see that b1b2/a1a2 < 0.
and that answers our question.
Drawing out each and every possibility on the graph is a tedious process.
I find the mathematical equivalent quite quick , if not simple.
a few general pointers
1. any linear equation of a line can be expressed as ax+by+c=0
ax+by = c
y-intercept is value of y when x =0 , i.e. y int= -c/b
x-intercept is value of x when y=0 , i.e. x int = -c/a
slope of a line passing through two points ( 0,-c/b) and (-c/a,0) is
(-c/b-0)/(0-(-c/a)) = - b/a
slope of a line = negative of y intercept / x intercept
its easier to remember this formula rather than its derivation.
FC wrote:Am wrong or the "point (4,3)" information is just irrelevant ?
From (I) (bl*bx)/(ml*mk)>0 (INSUF), from (II) bk*bl<0 (INSUF), so with both (I) and (II) together you can answer if ml*mk<0. So the info about (4,3) is not needed.
Thanks,
