Find the value of $p$ for which the lines, $px + 3y+5= 0$ and $8x + 2y - 3 = 0$ are parallel.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 12
For two lines to be parallel, their slopes must be equal.
Line 1:
$px + 3y + 5 = 0$
$3y = -px - 5 \Rightarrow y = -\frac{p}{3}x - \frac{5}{3}$
Slope $m_1 = -\frac{p}{3}$
Line 2:
$8x + 2y - 3 = 0$
$2y = -8x + 3 \Rightarrow y = -4x + \frac{3}{2}$
Slope $m_2 = -4$
Set slopes equal:
$-\frac{p}{3} = -4$
$p = 12$