When there is a condounder $Z$ for $X$ and $Y$, by plotting all three variables together, with each value of $(X, Y, Z)$ describing one point in space. In this case, the data will form a cloud of points in XYZ-space. The analogue of a regression line is a regression plane, which has an equation that looks like $Y = aX + bZ + c$. We can easily compute $a, b, c$ from the data.

The coefficient $a$ gives us the regression coefficient of $Y$ on $X$ already adjusted for $Z$. (It is called a partial regression coefficient and written $r_{YX.Z}$.)

If $Z$ is the only confounder, then a is the average causal effect of $X$ on $Y$.