Find the equation of a line perpendicular to line 2y = 5x + 4 which passes through (4, 2).
-
A.
5y – 2x -18 = 0 -
B.
5y + 2x – 18 = 0 -
C.
5y – 2x + 18 = 0 -
D.
5y + 2x – 2 = 0
Correct Answer: Option 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})
(frac{10 + 5}{5}) = c
y = -(frac{2}{5})x + (frac{18}{5})
5y = -2x + 18
or 5y + 2x – 18 = 0