Discussion
The equation of a straight line that passes through the point \((2, -5)\) and perpendicular to the line \(4x - y = 1\) is:
Answer: B
The line 4x - y = 1 has slope 4, so a perpendicular line has slope -1/4. Through (2, -5) its equation is
\[ \begin{aligned} y + 5 = -\tfrac{1}{4}(x - 2) \Rightarrow 4y + 20 \\ &= -x + 2 \Rightarrow x + 4y + 18 = 0 \end{aligned} \]The option 4x - y + 18 = 0 is parallel to the given line (same slope 4), x - 4y - 18 = 0 has slope 1/4, which is neither, and 4x + 3y - 9 = 0 has slope -4/3. Only x + 4y + 18 = 0 also passes through (2, -5): 2 - 20 + 18 = 0.
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