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# Find k such that the line 3x + ky = 17 is perpendicular to the line 8x - 5y = 26

Find k such that the line 3x + ky = 17 is perpendicular to the line 8x - 5y = 26

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Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
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Hi Ryan;
Both formulas are in Standard Format...
Ax+By=C  A>0, B>0
We need Slope-Intercept Format...
8x - 5y = 26
Let's subtract 8x from both sides...
-8x+8x-5y=-8x+26
-5y=-8x+26
Let's divide both sides by -5...
(-5y)/-5=[(-8/-5)x]+(26/-5)
y=(8/5)x+(-26/5)

The slope is 8/5
The perpendicular slope is -5/8.

3x + ky = 17
Let's subtract 3x from both sides...
-3x+3x+ky=-3x+17
ky=-3x+17
Let's divide both sides by k...
(ky)/k=[(-3/k)x]+(17/k)
y=(-3/k)x+(17/k)

-3/k=-5/8
Let's flip...
-k/3=-8/5
Let's multiply both sides by -3...
-3(-k/3)=(-8/5)(-3)
k=24/5

Kirill Z. | Physics, math tutor with great knowledge and teaching skillsPhysics, math tutor with great knowledge...
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Lines a1x+b1y+c1=0 and a2x+b2y+c2=0 are perpendicular if a1a2+b1b2=0.

In this case it means that 3*8-5k=0, from which it follows that k=24/5=4.8