boyle's law - graph

[amar21]

guys/gals

how come the graph listed in the review books for pressure/volume isnt a straight line going down?? Is it because the constant k in PV=k is making it curved?? IF thats the case, why isnt Charles law V/T = k also curved?

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[Vihsadas]

Think about what the dependent and independent variables are in each case, and, also about your knowledge of the different "forms" of an equation and what they look like.
Let's take the second case first.
The form of a linear equation is: Y = kX + b, where k is slope and b is intercept.

Charles law, V/T = k can be rearranged to:
V = kT + 0
Here, V is Y, T is X, k is slope and 0 is the intercept. So, this equation is linear.

Now think about boyle's law. Can you rearrange it to fit the form of a linear equation?

Well, no. You can't. The closest you can get is:

P = k/V.
This equation doesn't fit the form of linear equation, instead it fits the form of:
Y = k*(1/X) + b.

If you think about what this graph would look like, you'll see that as Y increases, X must decrease. Then, at Y = inf, the limit of X is zero. This means that the X variable must slowly tend to zero. So, that means that the graph must be curved. Do you see?