A couple notes: Usually people write the equation as either $y = b_0 + b_1X$ or $y = a + bx$ Your version is OK, but might be confusing when you see other versions.

In your equation, $a$ is a measure of how much $f(x)$ is expected to rise for a 1 unit increase in $x$. If $a$ is positive, then $f(x)$ is expected to rise as $x$ rises; if $a$ is negative, then just the reverse. So, $a$ is a measure of the slope. But $a$ is unit-dependent: If you change from measuring $x$ in millimeters to meters, $a$ will change, but its meaning will not.

There are a few measures of the strength of the relationship. The most common is $R^2$, this is a measure of the proportion of variance in $f(x)$ that is explained by the linear relationship with $x$.

A couple notes: Usually people write the equation as either $y = b_0 + b_1X$ or $y = a + bx$ Your version is OK, but might be confusing when you see other versions.

In your equation, $a$ is a measure of how much $f(x)$ is expected to rise for a 1 unit increase in $x$. If $a$ is positive, then $f(x)$ is expected to rise as $x$ rises; if $a$ is negative, then just the reverse. So, $a$ is a measure of the slope. But $a$ is unit-dependent: If you change from measuring $x$ in millimeters to meters, $a$ will change, but its meaning will not.

There are a few measures of the strength of the relationship. The most common is $R^2$, this is a measure of the proportion of variance in $f(x)$ that is explained by the linear relationship with $x$.

EDIT with regard to new question

A trend occur in units per time; there are several ways to standardize th units. You could, perhaps most simply, use percentage change from the beginning point. This is what is often done, e.g., with trend in stock market averages to accommodate their different initial values.