Find the equation of a line perpendicular to line 2y = 5x + 4 which passes through (4, 2).
- 5y - 2x -18 = 0
-
5y + 2x - 18 = 0
- 5y - 2x + 18 = 0
- 5y + 2x - 2 = 0
The correct answer is: B
Explanation
2y = 5x + 4 (4, 2)
y = \(\frac{5x}{2}\) + 4 comparing with
y = mx + e
m = \(\frac{5}{2}\)
Since they are perpendicular
m1m2 = -1
m2 = \(\frac{-1}{m_1}\) = -1
\(\frac{5}{2}\) = -1 x \(\frac{2}{5}\)
The equator of the line is thus
y = mn + c (4, 2)
2 = -\(\frac{2}{5}\)(4) + c
\(\frac{2}{1}\) + \(\frac{8}{5}\) = c
c = \(\frac{18}{5}\)
y = -\(\frac{2}{5}\)x + \(\frac{18}{5}\)
5y = -2x + 18
or 5y + 2x - 18 = 0
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