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*

Tutors, please sign in to answer this question.

Middletown, CT

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

Willowbrook, IL

Lines a_{1}x+b_{1}y+c_{1}=0 and a_{2}x+b_{2}y+c_{2}=0 are perpendicular if a_{1}a_{2}+b_{1}b_{2}=0.

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

Frank L.

Stat packages, data analyst, trainer/consultant

Jamaica, NY

4.9
(36 ratings)

Xinran W.

Columbia Graduate for Math and Chinese Tutor

New York, NY

Andleeb T.

Biochemistry major with STEP program mentoring experience

Fresh Meadows, NY

- Graph 155
- Math 8197
- Algebra 4439
- System Of Inequalities 40
- Math Help 4691
- Algebra 1 3588
- Algebra 2 3060
- Functions 568
- Inequalities 345
- Trigonometry 1291