The covariance is $s_{xy} = \frac{\sum (x_i - \bar x)(y_i - \bar y)}{n-1},$ where the sum is taken over $i = 1, \dots, n$ and $n$ is the
sample size. Then the correlation is
$r_{xy} = \frac{s_{x,y}}{s_x s_y},$ where $s_x$ and $x_y$ are the
two standard deviations.
If you have the regression line y = 13.555 -0.1688842 x. then you might say (over the interval of
your x data) that for each unit of increase in x
rate there is a decrease of about .17 units of y. In your second
regression line, I think you intend to have $y$ (not $x$) at the
end. In that equation you are expressing an increase of about .11
units of x for each unit of decrease in y. (However, it is customary
to use x on the horizontal axis and y on the vertical axis.)
For regression of y on x (with y's are on the vertical
axis, and to be predicted from x's), the estimated slope is $\hat \beta_1 = s_{xy}/s_x,$ so that
the units are those of y.
For regression of x on y (x on the vertical
axis, a 'nonstandard' situation) the estimated slope is $\hat \beta_1^\prime = s_{xy}/s_y,$ so that
the units are those of x.
Traditional statistical tests of the null hypotheses $\rho = 0,\,\beta_1 = 0,$
and $\beta_1^\prime = 0,$ (based on $r$, $\hat \beta_1$, and
$\hat \beta_1^\prime$, respectively) are mathematically equivalent.
Notes: This is intended to expand on the theme of @MichaelHardy's
answer. There is no necessity to bring a causal link between x and y into a 'philosophical' discussion.