Discussion

Find the value of k if the line \(kx + 3y - 1 = 0\) is parallel to the line \(2x + y + 5 = 0\).

Answer: C

For lines to be parallel, their slopes must be equal.

Slope of the first line \(kx+3y-1=0 \Rightarrow 3y = -kx+1 \Rightarrow y = (-k/3)x+1/3\). Slope m₁ = -k/3.

Slope of the second line \(2x+y+5=0 \Rightarrow y = -2x-5\). Slope m₂ = -2.

Set m₁ = m₂:

-k/3 = -2

k = 6.

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