Linearizing nonlinear relationships between x and y

[Oscar Zarate]

Homework Statement

You have the data of two measured variables x and y. According to a theory the variables relate to each other as the non-linear functions shown below where A is a constant. For each case, decide which variables you have to choose to plot so the expected graph is a straight line that passes through the origin.

Homework Equations

(a) y²= Ax³
(b) y³ = A √ x
(c) y² = A/x
(d) yx² = A

The Attempt at a Solution

I have attempted to move the x and y variables around as a way to cancel out exponents, but it has had no progression. I have also tried to input numbers, but it also has had no progression to it. I am not necessarily looking for an answer, but a push into the direction I should go with it.

 

[Chandra Prayaga]

Look at a simple relation like y = x^{2.
Think of x2 as a new variable z. What happens if you plot y vs. z?}

 

[haruspex]

decide which variables you have to choose to plot so the expected graph is a straight line that passes through the origin.

Perhaps you do not understand the question.
You are asked to define two new variables, call them X and Y. These are to be functions of the variables x and y. Likely X=X(x) and Y=Y(y), but not necessarily. A graph of Y against X needs to be a straight line through the origin.