Question 42663: Find the equation of the line through the given point that is perpendicular to the given line. 2y+6x-5=0 S(0,3)
Answer by tutorcecilia(2152)   (Show Source):
You can put this solution on YOUR website! To find the slope of line that is perpendicular to another line, take the reciprocal of the slope and multiply it by (-1).
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For example: If Slope #1 = a = a/1,
than Slope #2 of the perpendicular line = (1/a)(-1) = -1/a.
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First, write the equation in the slope-intercept format (y=mx+b)
Next, identify the slope of the first line.
Find the slope of the second line by inverting slope #1 and multiplying by (-1)
Plug-in the points (0,3) and solve for the y-intercept.
Write the slope-intercept equation for line #2.
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Line #1 = 2y+6x-5=0
y =-6x/2 -5/2
y = -3x-5/2
Slope (m1) = -3
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Line #2 has points (0,3) and slope (m2) = 1/3 (the reciprocal of Slope #1 multiplied by (-1)).
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Plug the values into the slope-intercept formula and solve for "b".
y =m x + b
3=(1/3)(0) + b
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Solve for b::
3=b
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Plug the slope and y-intercept back into the formula:
Line # 2: y=(1/3)x + 3
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