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In the xy-plane, line m passes through point (3,-2) and inte

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by Max@Math Revolution » Wed Jun 01, 2016 5:15 pm
In the xy-plane, line m passes through point (3,-2) and intersect perpendicularly with line n that passes through points (0,3) and (3,5). What is the equation of line m?
A. 3x+2y-5=0
B. 3x+2y+5=0
C. 2x-3y-12=0
D. 2x+3y=0
E. 4x+3y-6=0

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by ayushi21 » Thu Jun 02, 2016 5:38 am
the answers is A.
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by 800_or_bust » Thu Jun 02, 2016 5:48 am
Max@Math Revolution wrote:In the xy-plane, line m passes through point (3,-2) and intersect perpendicularly with line n that passes through points (0,3) and (3,5). What is the equation of line m?
A. 3x+2y-5=0
B. 3x+2y+5=0
C. 2x-3y-12=0
D. 2x+3y=0
E. 4x+3y-6=0

*An answer will be posted in 2 days.
Slope of the perpindicular line passing through (0,3) and (3,5):

m = (y2-y1)/(x2-x1) = (5 - 3)/( 3 - 0) = 2/3

Thus, the slope of our line is the negative reciprocal of this, that is -3/2.

To find the equation of this line...

y = mx + b

-2 = (-3/2)(3) + b
-2 = -9/2 + b
5/2 = b

y = (-3/2)x + 5/2

Rearranging to match the answer choices...

3x + 2y - 5 = 0 (Choice A)
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by Max@Math Revolution » Sun Jun 05, 2016 5:59 pm
If two lines intersect perpendicularly, we get -1 when we multiply two slopes together. The slope of a line n is (5-3)/(3-0)=2/3. Hence, the slope of a line m should be -3/2. Since it crosses (3,-2), if we calculate we get 3x+2y=5. Hence, the correct answer is A.
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