What is this equation for? $$t = \frac{r}{\sqrt{\frac{1-r^2}{n-2}}} \sim t_{n - 2}$$
with $$r = \frac{S_{xy}}{\sqrt{SC_{xx} SC_{yy}}}$$
I've just found this equation with no direct data to of what can I get from it, I couldn't get what is it use for, but I know that is relate to Pearson.
In the same diapositive, it says proof of hypothesis for $p$
$H_0$: $p=0$, there is no relation between variables
$H_1$: $p \neq 0$ there IS a relation between variables
but there it is called $p$, while the equation it says, $t$, so I assumed, there were not the same thing

This is a hypothesis test for the significance of a correlation coefficient, though it is equivalent to a test for the slope in a simple linear regression. See here, for example. The first formula is the test statistic, while the second one is the sample correlation.
That should be a $\rho$ (population correlation) rather than a $p$ in your null and alternative hypotheses.
You have a bivariate sample $(x_1,y_1), \ldots, (x_n, y_n)$, where the $X$ and $Y$ variables are jointly normally distributed, and $r$ is the sample correlation. Under a null hypothesis of $\rho=0$ (no correlation between the two variables), your test statistic $t$ is $t$-distributed with $n-2$ degrees of freedom.
