Find the value of p, if the line that passes through (-1, -p) and (-2p, 2) is parallel to the line 2y + 8x - 17 = 0
A
\(\frac{7}{6}\)
B
\(\frac{6}{7}\)
C
\(\frac{-2}{7}\)
D
\(\frac{-6}{7}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
The given line is 2y + 8x - 17 = 0.
Rewrite in slope form: 2y = -8x + 17
y = -4x + \(\frac{17}{2}\)
Slope = −4.
The line through points \((-1, -p)\) and \((-2p, 2)\) must have the same slope (parallel lines).
Slope = \(\frac{2 - (-p)}{-2p - (-1)} = \frac{2 + p}{1 - 2p}\)
\(\frac{2 + p}{1 - 2p} = -4\)
Cross-multiply:
2 + p = -4(1 - 2p)
2 + p = -4 + 8p
2 + 4 = 8p - p
6 = 7p
p = \(\frac{6}{7}\)
Source: Myschool Past Questions Archive (Record #76327)