$\displaystyle ay^2=(x+b)\ln x$
How do I change this equation to the form Y=mX+c? where do I start?
a, and b are constants.
Thanks
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.