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: 5y + 2x - 18 = 0
Explanation
2y = 5x + 4 (4, 2)
y = 5x/2 + 4 comparing with
y = mx + e
m = 5/2
Since they are perpendicular
m1m2 = -1
m2 = −1/m1 = -1
5/2 = -1 x 2/5
The equator of the line is thus
y = mn + c (4, 2)
2 = -2/5(4) + c
2/1 + 8/5 = c
c = 18/5
y = -2/5x + 18/5
5y = -2x + 18
or 5y + 2x - 18 = 0
2y = 5x + 4 (4, 2)
y = 5x/2 + 4 comparing with
y = mx + e
m = 5/2
Since they are perpendicular
m1m2 = -1
m2 = −1/m1 = -1
5/2 = -1 x 2/5
The equator of the line is thus
y = mn + c (4, 2)
2 = -2/5(4) + c
2/1 + 8/5 = c
c = 18/5
y = -2/5x + 18/5
5y = -2x + 18
or 5y + 2x - 18 = 0