Drawing draw guide lines with known slope on a scatter plot

Question

I'm pretty new to using seaborn. I'm trying to add custom lines (nothing like regression or anything like that) to this scatter plot:

enter image description here

This is the code I'm using for plotting the data:

sns.set(font_scale=2, style='ticks')
plt.figure(figsize=(7, 10))
plt.xscale('log')
plt.yscale('log')

sns.scatterplot(data=degrees_2020, x="degree_20", y="len", legend = "full")
sns.scatterplot(data=degrees_2019, x="degree_19", y="len", legend = "full")
sns.scatterplot(data=degrees_2018, x="degree_18", y="len", legend = "full")
sns.scatterplot(data=degrees_2017, x="degree_17", y="len", legend = "full")
plt.legend(loc = 'lower right', labels=["2021","2020","2019", "2018"])

plt.show ()

And this one of the dataframes:

  degree_20  len
1       16  1581
2       16  1581
3       16  1581
4       16  1581
... ... ... ...
1705        32  1926
1706        57  2196
1707        44  2098
1708        95  2246
1709        131 2286

This is the code I used for generating the scatter plot. Basically, I want to add two lines, just to guide the eye not fitting the data points. These two for example, would be len~k and len~k^{2 .}

I can't find a way to custom-add these two lines to the plot using seaborn. I'm wondering if it's doable and if you have any tips or ticks I'd appreciate it.

Many thanks!