Is the angle of a line from the bottom-right to the top-left of a graph always $45$ degrees?

Question

I have a theory. Let's say we have a graph, and a line from the bottom-right to top-left

\
 \
  \
y  \ 
    \
     \
      \
     x axis

Knowing that a straight vertical line is perpendicular and $90$ degrees, I think a diagonal line would always be $45$ degrees right?

This is assuming $x$ and $y$ are equal.

Also, is there a general formula for calculating the angle of a line from point $a$ to point $b$?

Let's say we wanted to calculate the angle of a line from the bottom-right to the middle like this

---- This is in the space of our graph
----
----
\
 \
  \

Now instead of moving from lower right to upper left, we're moving somewhere to the middle. How can we calculate the angle between the lines?

Answer 1

If the line is $y=x$ then $x$ and $y$ are always equal. So the answer to the question in the title is yes if and only if the equation of the line is $y=x$. So the angle of the line $y=x$ will be $45^{\circ}$ to any line parallel to the $y$-axis.