SOLUTION: Find an equation of the line satisfying the given conditions. Through (-4,3); perpendicular to -8x+5y=77

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Question 201322: Find an equation of the line satisfying the given conditions.
Through (-4,3); perpendicular to -8x+5y=77
Found 2 solutions by Earlsdon, RAY100:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Recall that if two lines are perpendicular, then their slopes are the negative reciprocal of each other, that is: m%5B2%5D+=+-1%2Fm%5B1%5D
Let's find the slope of the given line:
-8x%2B5y+=+77 Solve this equation for y so that you have it in the slope-intercept form: y+=+mx%2Bb. Add 8x to both sides.
5y+=+8x%2B77 Now divide both sides by 5.
y+=+%288%2F5%29x+%2B+77%2F5 Compare this with:
y+=+mx%2Bb and you can see that the slope m%5B1%5D+=+8%2F5.
The negative reciprocal of m is:
m%5B2%5D+=+-1%2Fm%5B1%5D
m%5B2%5D+=+-%281%29%2F%288%2F5%29
highlight%28m%5B2%5D+=+-5%2F8%29 so, for the new equation, you can start by writing:
y+=+%28-5%2F8%29x%2Bb To find the value of b, you need to substitute the values of the x- and y-coordinates of the given point (-4, 3) and solve for b.
3+=+%28-5%2F8%29%28-4%29%2Bb Simplify.
3+=+%285%2F2%29%2Bb Subtract 5%2F2 from both sides. Replace(3+=+6%2F2)
%286%2F2%29-%285%2F2%29+=+b or...
b+=+1%2F2 Now you can write the final equation.
highlight%28y+=+%28-5%2F8%29x%2B1%2F2%29

Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
For this problem, lets first find the slope of the original equation, using y=mx +b form, and then define the slope of the second eqn as, m2=-1/m1,perpendicular. Finally, we can define the eqn of the second line from the slope and the given point.
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-8x +5y =77
5y = 8x +77
y = (8/5)x + 77/5
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or from form ,,,,y= m x +b,,,m = (8/5)
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m2= - 1/m1 = (-5/8)
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Second eqn is , y= mx +b,,,,y = (-5/8) x +b
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As it contains the point ( -4,3),,,,substitute
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(3) = (-5/8) (-4) + b
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3 = 20/8 +b
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24/8 - 20/8 = 4/8 =1/2 = b
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subst m,,and b,,in form eqn,, y = (-5/8)x + (1/2)
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mult thru by 8
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8y = -5x + 4
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checking, subst ( -4,3),,,,8*3=(-5)(-4) +4 = 24 ,,,,ok