Question

If the lines 2x + 3y = 5 and kx – 6y = 7 are parallel, then what is the value of k?

• A. -4

Answer 1

The correct option is A -4
Lines 2x + 3y = 5 and kx – 6y = 7 are parallel

Slope of 2x + 3y = 5
$\Rightarrow 3y=-2x+5$
$\Rightarrow y=\frac{-2x}{3}+\frac{5}{3}$

$\therefore$ The slope is $\frac{-2}{3}$

Slope of $kx–6y=7$
$\Rightarrow y=\frac{kx}{6}+\frac{7}{6}$
$\therefore$ The slope is $\frac{k}{6}$

Now, since both lines are parallel then, their slopes are equal.
$\frac{k}{6}=\frac{-2}{3}$
$k=\frac{-2}{3}\times 6$
$k=-4$