# Thread: Change the form to y=mx+c

1. ## Change the form to y=mx+c

$\displaystyle ay^2=(x+b)\ln x$

How do I change this equation to the form Y=mX+c? where do I start?
a, and b are constants.
Thanks

2. 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?

3. 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)$\displaystyle y=a^{x+b}$
(b)$\displaystyle ay^2=(x+b)\ln x$
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.

4. What do you know of "Least Squares Estimation" and "Normal Equations"?

5. Okay, I'll take Orthogonal Projection onto a Vector Space.

6. I have not studied any of the mentioned before

7. 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)$\displaystyle y=a^{x+b}$
(b)$\displaystyle ay^2=(x+b)\ln x$
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 $\displaystyle ay^2=(x+b)\ln x$, where a and b are constants. Write the equation in the form $\displaystyle a\Bigl(\frac{y^2}{\ln x}\Bigr) = x+b$. That suggests that you should put $\displaystyle z = \frac{y^2}{\ln x}$. 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.