Finding the slope and intercept of a graph

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SUMMARY

The discussion centers on determining the slope and intercept of a graph plotting ln(A) against ln(3d²) based on the formula A = Bt / (3d²). The transformation of the equation leads to ln(A) = ln(Bt) - ln(3d²), allowing for the identification of the slope as -1 and the intercept as ln(Bt). This analysis provides a clear method for understanding the linear relationship between the logarithmic variables.

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Homework Statement


I am given the formula A = Bt / (3d2)

d is what we changed, A is what was measured.

I had to plot ln(A) vs ln(3d2).

What do the slope and intercept of this graph represent?

Homework Equations





The Attempt at a Solution


ln (A) = ln (Bt / 3d2) = ln(Bt) - ln(3d2)

ln (A) / ln (3d2) = ln (Bt)/ln(3d2) - 1

After this I get stuck. Help please!
 
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jumbogala said:

The Attempt at a Solution


ln (A) = ln (Bt / 3d2) = ln(Bt) - ln(3d2)

ln (A) / ln (3d2) = ln (Bt)/ln(3d2) - 1

After this I get stuck. Help please!

If you are plotting ln(A) vs. ln(3d2), then let

x = ln(3d2)
y = ln(A)​

and you are now plotting y vs. x.

Write your equation,

ln (A) = ln(Bt) - ln(3d2),​

in terms of x and y. The slope and intercept should become easier to identify.
 

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