# Change the form to y=mx+c

• Mar 1st 2010, 06:38 PM
arze
Change the form to y=mx+c
$ay^2=(x+b)\ln x$

How do I change this equation to the form Y=mX+c? where do I start?
a, and b are constants.
Thanks
• Mar 1st 2010, 07:26 PM
TKHunny
Truthfully? Since it isn't possible to do what you have suggested, you may wish to review what it is you have been asked to do.

Can you supply the COMPLETE problem statement rather than your abbreviated version?
• Mar 1st 2010, 07:44 PM
arze
Ok here's the whole question:
In an experiment, sets of values of the related variables (x,y,) are obtained. State how you would determine whether x and y were related by a law of the form:
(a) $y=a^{x+b}$
(b) $ay^2=(x+b)\ln x$
where in each case, a and b are unknown constants. State briefly how you would be able to determine the values of a and b for each law.
• Mar 2nd 2010, 07:53 AM
TKHunny
What do you know of "Least Squares Estimation" and "Normal Equations"?
• Mar 2nd 2010, 01:42 PM
TKHunny
Okay, I'll take Orthogonal Projection onto a Vector Space.
• Mar 2nd 2010, 03:52 PM
arze
I have not studied any of the mentioned before
• Mar 3rd 2010, 12:39 AM
Opalg
Quote:

Originally Posted by arze
Ok here's the whole question:
In an experiment, sets of values of the related variables (x,y,) are obtained. State how you would determine whether x and y were related by a law of the form:
(a) $y=a^{x+b}$
(b) $ay^2=(x+b)\ln x$
where in each case, a and b are unknown constants. State briefly how you would be able to determine the values of a and b for each law.

So you have (from the experiment) a set of values of x and the corresponding values for y. In (b), you want to know whether x and y are related by an equation of the form $ay^2=(x+b)\ln x$, where a and b are constants. Write the equation in the form $a\Bigl(\frac{y^2}{\ln x}\Bigr) = x+b$. That suggests that you should put $z = \frac{y^2}{\ln x}$. For each pair of values (x,y), calculate the corresponding value of z. Then plot a graph of z against x. Hopefully the points will look as though they lie on a straight line, with equation az = x+b.