Question

if the two straight lines 2x-3y+9=0,6x+ky+4=0 are parallel,find k

Answer 1

If two straight lines are parallel, their slopes are equal.
therefore, 2/3 = -6/k
or, k = - 18/2 = - 9

Answer 2

I
$\frac{2}{6} = \frac{3}{k} \: is \: not = \frac{9}{4}$
f the two straight lines are parallel then there exist a formula

a1/a2 = b1/b2
$\frac{a1}{a2} = \frac{b 1}{b2} is \: not \: equal \: to \: \frac{c1}{c2}$

here a1 = 2 b1 = -3 c1 = 9

and a2 = 6 b2 = k and c2 = 4

=} 2k = -18 ( by cross multiplication)

=) k = -9
Hence k = -9

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