Question

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

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

Hint:

Two lines are parallel if and only if their slopes are equal.

Answer 1

The Correct Option is B

For the lines to be parallel, they must have the same slope. The equation of a straight line \( ax + by = c \) has a slope of \( -\frac{a}{b} \). For the first line, \( 4x + py = 16 \), the slope is: \[ \text{slope}_1 = -\frac{4}{p}. \] For the second line, \( 2x + 9y = 15 \), the slope is: \[ \text{slope}_2 = -\frac{2}{9}. \] Since the lines are parallel, their slopes must be equal: \[ \frac{4}{p} = \frac{2}{9}. \] Solving for \( p \): \[ p = \frac{4 \times 9}{2} = 18. \] Thus, the value of \( p \) is \( \boxed{3} \).