equation of a line perpendicular to y=3x-1?

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- anonymous

equation of a line perpendicular to y=3x-1?

- katieb

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- anonymous

perpendicular line is the negative reciprocal
so the slope of the line has to be
\[-\frac{1}{3}\]
since there's no point, you can put any constant or you can just leave it at zero
\[y = -\frac{1}{3}x\]

- anonymous

what do you mean since there's no point? what about the -1?

- myininaya

hes says your question did't say what point the perpendicular line was running through

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- anonymous

the -1 is the intercept for y = 3x -1
but the question asks you for equation of A line, so ANY line
it can be y = -(1/3)x
or
y = -(1/3)x + 3
y = -(1/3)x + 5
it can be any number
because the question doesn't specify a specific point that the line has to go through

- anonymous

it says it has to pass through the point of intersection from these two equations:
y=24/x and y=3x-1

- myininaya

y=-(1/3)x+C where C is a constant is the general perpendicular line for the line y=3x+K where K can be any constant

- anonymous

it has to pass through the point where those two equations intersect?

- anonymous

yes

- myininaya

set 24/x=3x-1

- myininaya

solve for x

- anonymous

so set those equations equal to one another and solve for the point
24/x = 3x - 1
3x^2 -x = 24
3x^2 - x - 24 = 0
x = -(8/3), 3
myininaya, what am i doing wrong? how can i get two intersections for two lines???

- myininaya

24/x is not a line its a hyperbola

- anonymous

oh wait yeah, i didn't catch that..

- myininaya

so since we have two intersections and your question didn't specify which intersection we have 2 equations:
they both have the the form y=-(1/3)x+C
so we have 1 equation with x=-8/3 so y=3(-8/3)-1=-9 so we have -9=-(1/3)(-8/3)+b
solve for b to find the y intercept
and we also have equation 2 with x=3 so y=3(3)-1=8 so we have 8=-(1/3)(3)+b solve this for b
and you have your two equations

- myininaya

so the first equation we have -9-8/9=b so b=-89/9 so equation 1 is y=-(1/3)x-89/9 and the second equation we have 8+1=b so b=9 so equation 2 is y=-(1/3)x+9

- anonymous

thank you !

- myininaya

your welcome. what class is that? is that really algebra? That is hard question for algebra students. no offense. i would know since I teach algebra

- myininaya

i like it though. I might give it as a project hehe

- anonymous

ib math studies :)

- myininaya

ib?

- anonymous

International Baccalaureate its a higher level of math offered worldwide

- myininaya

i am jealous

- myininaya

i wish i was challenged more but I guess I know enough lol, but no one could really know enough so I take that back

- anonymous

its like college level math. well all of my courses are ib.

- myininaya

so did you understand everything above?

- anonymous

this is supposed to be an easy problem compared to the other problems we learn lol yes i did thank you !

- myininaya

i really liked your problem. its nice

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