117k views
0 votes
What is the slope of a line perpendicular to 8x+9y=1

User Nory
by
8.6k points

2 Answers

4 votes
The slope of a line that is perpendicular is the negative reciprocal.
In slope intercept form the line you gave is y= -8/9x+1/9.
So the slope is -8/9.
Meaning the slope of a line that is perpendicular would be 9/8.
User BlackMagic
by
7.2k points
5 votes
If put into slope intercept form...y=mx+b where m=slope

8x+9y=1

9y=-8x+1

y=(-8x+1)/9

So the slope is -8/9

For a line to be perpendicular to this one, it must have the negative reciprocal slope of the reference line:

Mathematically, for two lines to be perpendicular to each other:

m1*m2=-1 in this case:

-8m/9=-1

m=-9/-8

m=9/8 or if you prefer

m=1.125

For your curiosity...since slope equals dy/dx we can say that:

tanα=(dy/dx) and in this context

tanα=m so the angle is:

α=arctan(m)

a=arctan(-8/9)≈-41.63

b=arctan(9/8)≈48.37

So the difference between b and a is 48.37--41.63=90° Since they are at a 90° to each other, they are perpendicular...
User Hamid Ghasemi
by
7.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories