Math Is Fun Forum

nostalgia

Member

Registered: 2009-07-31

Posts: 1

Help me please! Linear law question?!

Hi I'm having a little trouble with this topic. Heres a question that i couldn't figure out for hours;
The table shows experimental values of two variables x and y.

Heres the table :
x : 0.5 1.0 2.0 4.0 10.0
y: 2.2 3.6 5.1 6.5 7.8

It is known that x and y are related by an equation of the form y=ax/x+b. Using the vertical axis for y and the horizontal axis for y/x, draw a straight line graph of y against y/x for the given data.
Use the graph to estimate:
(i) the value of a and of b.
(ii) the value of x for which y=3x

so i was stuck at (i) .. basically I drew a table for y against y/x

y/x : 4.4 3.6 2.55 1.63 0.78 <-- why is it that it's not in 1dp form?
y: 2.2 3.6 5.1 6.5 7.8
the thing is, I'm confused as to whether I'm suppose to round it off to 3 significant figs or 1 decimal place?? When I plot out the graph I get a different gradient than the answer sheet.

y= ax/x+b
yx+yb=ax
yx/x + yb/x = a
y + yb/x = a
y= -yb/x + a
y= -b(y/x) + a (The form of y=mx+c)

So my gradient should be negative right, since it's a -b now.
But the thing is when I plot out the graph i get an answer of -1.75 whereas the answer sheet writes -1.53??

Where did I go wrong? Thanks for your time.

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Hi, I'm just your average high schooler trying my very best to cope with math. It's pretty fun but sometimes things get challenging and well, Yeah I really need help - That's why I'm here right? I try to help others the best I can too, sorry If I screw things up though.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help me please! Linear law question?!

Hi nostalgia;

First is this a typo?

y=ax/x+b

Which of these do you mean?

When I do a linear fit of the data I get the equation y= -1.529 (x/y) + 9. So the worksheet looks right.

Last edited by bobbym (2009-08-01 01:27:33)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Fruityloop

Member

Registered: 2009-05-18

Posts: 143

Re: Help me please! Linear law question?!

I think he means y=ax/(x+b).

But, there seems to be something wrong with the numbers listed for x and y from the table.
I figured out a=9.9 and b=1.75 using x=0.5, y=2.2  and x=1.0, y=3.6, but those values for a and b don't work for the other values in the table, like x=10.0  y=7.8.

Last edited by Fruityloop (2009-08-01 01:20:30)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help me please! Linear law question?!

Hi fruityloop;

I think he means y/x. He has linearized the points by the transformation y/x -> x. But you might be right.

y/x : 4.4 3.6 2.55 1.63 0.78 <-- why is it that it's not in 1dp form?
y: 2.2 3.6 5.1 6.5 7.8

etc.

Last edited by bobbym (2009-08-01 06:59:57)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.