Wednesday, October 17, 2007

Today's Slides: October 17

Here they are ...


«Craig» said...

I got it! very good question it made me think fairly hard about it.
However, I don't think that everyone has had sufficient time to look at it, so I won't post my answer until after me Scribe post, which will be a little bit later tonight =)

m@rk said...

WOW, I seriously just don't get this question. The only thing that i know is that c is the slope because it is the derivative. Other than that the last question seems to make no sense to me.So my answer will be:


I don't know if that makes sense. Now back to some serious studying for our pretest.

aichelle s. said...

hmm well after some thinking I think that it's:

f(x) = cx + (b-a)

However, I don't know if I am correct. It worked for the previous questions that we did in class.
I honestly don't know how to explain how I got that but c is the slope. The only reason why I had b - a is because I was trying to figure out what I could get to get f(x). I don't know how to explain why it works.

m@rk said...

I was thinking of that same function at first but i just couldnt explain the (b-a) part, thats why i just sticked with my guts. This question is tough. I think i'm just gonna ask my sister when she gets home.

«Craig» said...

Well, here goes...

Now, I'm looking at the other possible answers and wondering if mine might be wrong, but I got:

f(x) = cx + (b-ac)

Now, my explanation?..

Well to find the equation of a line all that is needed is the slope and the y-intercept. Now we are already given the slope (f'(x)=c). Now all we need is the intercept. Well we know one point (a,b) so to find the intercept:
-first, find the distance from the point(a,b) to (0,b). Obviously it's a.
-next, since the slope is the change in y over the change in x, and you already know the change in x and the slope, you can use:

slope = ∂y / ∂x
c = ∂y / a
∂y = c • a

-So now the y coordinate of the y-intercept is the y coordinate(b) subtract ∂y. (b - ca)
-Now that we have the slope and y-intercept, plug it into the equation of a line to get:

f(x) = m • x + y-int.
f(x) = c • x + (b - c • a)
f(x) = cx + (b-ac)

WOW, that could have been a scribe post in itself LOL... Oh well, I hope everyone understands =)

«Craig» said...

BTW Aichelle, you were so close, you just forgot to multiply a by c because you only used the previous questions as examples (all slopes of 1 so c=1) You had it!

aichelle s. said...

haha oh! nice thanks for explaining it you're so smart Craig!

m@rk said...

wow! I got it now but i have a different explanation.

If f(x) = c then the f(x) = cx + m, where m is some constant. We also know that f(a) = b which means
f(a) = ca + m = b solve this for m to get
m = b - ca. Put this into the equation for f(x) and you get

f(x) = cx + b - ca

(All the credits belong to the person who helped me on yahoo answers)

Tim_MATH_y said...

After looking at all the collective comments, I find that I totally agree with your answer, Craig and Mark.

Craig's definition was more in depth it seems yet hard to follow. However, I loved the explanation you came up with MArk!

However, good job to you all for your efforts =)