for a line with the points (3,3) and (4,k) what are the values of k that would make the slope undefined

- ineedhelp10

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- anonymous

Do you know what makes a slope undefined?

- ineedhelp10

yeah its when the slope ends up being error

- anonymous

It's when the denominator is equal to 0. That is, there is no change in x. A vertical line

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## More answers

- anonymous

do you know the equation for the slope of a line given two points?

- ineedhelp10

yeah its y2-y1/x2-x1

- anonymous

ok so plug in the numbers you have into that equation

- anonymous

There is a change in x of 1 unit

- anonymous

so there is no y value that can make it undefined

- ineedhelp10

okay but what do i set it equal to?

- anonymous

(k-3)/(4-3) = (k-3)/1

- anonymous

No k value makes the slope undefined

- anonymous

Do you see what I mean?

- ineedhelp10

would it be k-3?

- anonymous

the slope is undefined if x2-x1 = 0, correct?

- ineedhelp10

wait would it be all real numbers?

- anonymous

no

- anonymous

for the slope to be undefined, x2-x1 must equal 0, right?

- anonymous

(y2-y1)/(x2-x1)
(x2-x1) is the denominator. If (x2-x1) = 0, then the slope is undefined.

- anonymous

right?

- ineedhelp10

okay so then what?

- anonymous

well x2=4 and x1=3 so (x2-x1) = 1
No y value will change that. So the slope cannot be undefined

- ineedhelp10

okay so then what would that make the value of k?

- anonymous

Are you sure you typed the problem right? It would make more sense if it asked about (3,3) and (k.4)

- ineedhelp10

yeah i typed it right

- anonymous

changing k won't change the value of the denominator. So there is no value of k that would make the slope undefined.

- ineedhelp10

okay you're so sure

- anonymous

it's either a trick question or your teacher made a mistake

- ineedhelp10

and for the slope to be 0 would it have to be 3

- anonymous

correct

- ineedhelp10

okay thank you so much!!

- anonymous

No problem

- ineedhelp10

wait for the undefined would it be all real numbers?

- anonymous

That would mean that the slope is always undefined
It is never undefined

- ineedhelp10

so then what can i say as my final answer?

- anonymous

I would say that no value of k makes the slope undefined

- ineedhelp10

okay thehn thank you again!!

- anonymous

Of course

- ineedhelp10

wait what can i say for my explanation lol my bad

- ineedhelp10

do you know?

- anonymous

There is no value of k that makes the slope undefined.

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