Question

If the lines \( 4x + py = 16 \) and \( 2x + 9y = 15 \) are parallel, then the value of \( p \) is:

• A. \( \frac{1}{3} \)
• B. \( 3 \)
• C. \( 18 \)
• D. \( -3 \)

Answer 1

The Correct Option is C

For two lines \( a_1x + b_1y + c_1 = 0 \) and \( a_2x + b_2y + c_2 = 0 \) to be parallel, their slopes must be equal:
\[ \frac{a_1}{a_2} = \frac{b_1}{b_2}. \] Rewriting the given equations:
\[ 4x + py = 16 \quad \Rightarrow \quad a_1 = 4, \quad b_1 = p. \] \[ 2x + 9y = 15 \quad \Rightarrow \quad a_2 = 2, \quad b_2 = \] Setting the slope ratios equal:
\[ \frac{4}{2} = \frac{p}{9}. \] \[ 2 = \frac{p}{9}. \] Solving for \( p \): \[ p = \]