Finding the slope and intercept of a graph

[jumbogala]

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!

 

[Redbelly98]

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.

 

[kerimek]

The slope and intercept of a graph represent important characteristics of the relationship between the variables being plotted. In this case, the graph is plotting ln(A) against ln(3d2), which suggests that there is a logarithmic relationship between A and 3d2. The slope of the graph represents the rate of change between ln(A) and ln(3d2), or the change in ln(A) for every unit change in ln(3d2). This can also be interpreted as the power to which 3d2 needs to be raised to get A. The intercept of the graph represents the value of ln(A) when ln(3d2) is equal to 0, or when d is equal to 0. This can also be interpreted as the initial value of A when d is equal to 0. In summary, the slope and intercept of the graph provide important information about the relationship between A and d, and can be used to make predictions and draw conclusions about the data.