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Question 63097: Find the equation of the line passing through the point (-1,6) and parallel to the line -2x+y=9 and B) perpendicular to the line -2x+y=9
thank you
Answer by uma(370)   (Show Source):
You can put this solution on YOUR website! (A) Equation of the given line is -2x + y = 9
In the slope intercept form the above equation can be written as y = 2x + 9
Slope of this line = 2
So slope of any line parallel to this line = 2 as parallel lines have equal slopes.
The required line has a slope of 2 and passes through (-1,6)
The equation is y - 6 = 2(x - (-1))
==> y - 6 = 2(x+1)
==> y - 6 =2x + 2
==> y - 6 + 6 = 2x + 2 + 6
==> y = 2x + 8 is the required equation.
(B) The given line is 2x + y = 9
THis is rewritten as y = - 2x + 9
Slope of this line = -2
[as product of slopes of perpendicular lines = -1]
slope of the perpendicular line = -1/-2
= 1/2
The required line passes through (-1, 6)
The required equation is y - 6 = 1/2 (x + 1)
==> 2(y-6) = 1(x + 1)
==> 2y - 12 = x + 1
==> 2y - 12 - x - 1 = 0
==> -x + 2y - 13 = 0
Good Luck!!!
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