How to find the gradient and intersection in a log-log plot?

Hi. I want to find the gradient and intersection point of a log-log plot.
I have the following data:
a=[51.2;69.5;94.5;128.5]
b=[12.12;11.12;10.21;9.34]

I then plotted a vs. b in a log-log plot. I want to find the gradient in the log-log plot and the intersection point where x=0. I can do this without using the graph itself by using the following excel-formula:
SLOPE(LOG(F15:F18);LOG(E15:E18)). Then I got -0.28 as the gradient. The expression for the trendline: y=-0.2.896*ln(x)+23.397. There I got the point where it crosses the y-axis. But I do not get the gradient and the point where the line crosses the y-axis? Does anyone know how I can do it graphically by using "least-squares" method?

Regards,
David

Does anyone know how I can do it graphically by using "least-squares" method?

What is your question here? Performing a regression "graphically by using "least-squares" method" would be by charting the data on an XY scatter plot and adding a trendline, which it sounds like you have already done. I tend to prefer using the LINEST() equation to perform these linear regressions, but the SLOPE() and INTERCEPT() functions can work just fine as well.

I also sense some confusion about equations (not necessarily Excel questions), that maybe are the real questions you are asking.
For a power trendline (a straight line on a log-log plot), I get y=(10^1.5667)*x^-0.2863 or y=exp(3.608)*x^-0.2863 depending on whether I use common log or natural log.
For the logarithmic trendline you describe, I get y=-6.9423*log(x)+23.950 or y=-3.015*ln(x)+23.950.
So I think the first question might be -- what regression equation are you trying to use -- a power trendline (straight line on a log log plot) or a logarithmic trendline (which would be a straightline on a semi-log plot)?

Gradient should be straightforward, if you remember your calculus. Use calculus to derive the desired expression for the gradient, then enter that formula into Excel.

Intercepts might be tricky, in part because 0 is a problematic value for these equations.
For these power trendlines, y and x can never be 0 (assuming real numbers). ln(y) and ln(x) can be 0 [y=1 or x=1], so you can find these "intercepts", and that should be simple algebra.
For the logarithmic trendline, y can be 0, and should be easily solved for algebraically. x, however, cannot be 0.