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Which of the following is an equation of the straight line that has y-intercept 2 and is perpendicular to the line 3x – 5y = 11?
(A) 5x – 3y = 2
(B) 5x + 3y = 2
(C) 3x – 5y = 9
(D) 3x – 5y = –10
(E) 5x + 3y = 6
_________________
(A) 5x – 3y = 2
(B) 5x + 3y = 2
(C) 3x – 5y = 9
(D) 3x – 5y = –10
(E) 5x + 3y = 6
_________________
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Given,
Line must have a y-intercept of 2
and perpendicular to line L1: 3x - 5y = 11
Consider standard equation of line: y = mx + c, where
m = slope
c = y-intercept
L1: y = (3/5)x - (11/5)
L2: y = (m2)x + c2
According to given information,
c2 = 2
and since two lines L1 and L2 are perpendicular,
m1*m2 = -1 where m1 and m2 are slopes of L1 and L2 respectively
=> (3/5)*(m2) = -1
=> m2 = -5/3
L2: y = (-5/3)x + 2 => 3y = -5x + 6 => 5x + 3y = 6
Hence E
Line must have a y-intercept of 2
and perpendicular to line L1: 3x - 5y = 11
Consider standard equation of line: y = mx + c, where
m = slope
c = y-intercept
L1: y = (3/5)x - (11/5)
L2: y = (m2)x + c2
According to given information,
c2 = 2
and since two lines L1 and L2 are perpendicular,
m1*m2 = -1 where m1 and m2 are slopes of L1 and L2 respectively
=> (3/5)*(m2) = -1
=> m2 = -5/3
L2: y = (-5/3)x + 2 => 3y = -5x + 6 => 5x + 3y = 6
Hence E
Bunuel
POE method:
Two condition laid out here are-
1. y-intercept is 2
2. the required line must be perpendicular to 3x - 5y = 11(m = 3/5)
For y-intercept to be 2 we need coefficient of y to be a multiple of y-intercept when x = 0.
Upon checking we see that A,B and C are out. Only D and E fulfil the 1st condition.
For 2nd condition, E has a slope of -5/3.
Answer E.
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