Let's say I had a graph for some experiment that we thought was modelled by a = bcd + g. If we perform an experiment and plot a vs. c, what do we expect the slope and intercept to be?

Would intercept = g
and slope = b ?

If that's right, what would d represent?

when c=zero, a=g so the x intercept is g, and the slope is bd

To determine the expected slope and intercept when plotting a vs. c for the equation a = bcd + g, we need to rearrange the equation to the form of a linear equation: a = mx + b, where m is the slope and b is the intercept.

Considering the equation a = bcd + g, we can rewrite it as:
a = bc(d) + g

Now, if we plot a vs. c, we consider c as the independent variable (x-axis) and a as the dependent variable (y-axis). Therefore, we need to isolate a on one side of the equation.

Rearranging the equation, we have:
a - g = bc(d)

Comparing this to the linear equation form a = mx + b, we find:
m = bc, which represents the slope.
b = a - g, which represents the intercept.

So
slope (m) = bc
intercept (b) = a - g

Regarding the variable d in the original equation a = bcd + g, it represents a variable introduced in the model. The meaning or interpretation of d would depend on the context of the experiment or the specific system being studied. Without further information, it is not possible to determine what d represents in this scenario.