What is the value of r if the slope of the regression line is steeper than 1? What would be the value of r if the slope was steeper than in the leftmost diagram? Is r the slope or is it just proportional to the slope? Does it have anything to do with the quality of the regression (i.e., how much do the data points scatter around the regression line? - I think that is what r^2 is for, right?)


On its own, the slope tells you nothing about how good the fit is (unless the slope is exactly zero). If $\hat y_i =\hat\beta_0 + \hat\beta_1x_i$:
$$
\hat\beta_1=r \dfrac{
s_y
}{
s_x
}
$$
In the above, $r$ is the observed correlation, $s_y$ is the observed (sample) standard deviation of $y$,and $s_x$ is the observed (sample) standard deviation of $x$.
Without knowing the ratio of standard deviations, the slope and correlation tell you nothing about one another besides the sign. (Assume you’re not in a silly situation where $y$ or $x$ are constant.)
