fitted regression line interpretation? Like interpret the intercept and slope in a practical context of the data. For example, if I am given this fitted regression line $$Y\hat = -0.55 + 0.09X$$
Where X is a SAT score  and Y is a GPA. Basically estimating GPA given SAT score by using this formula. interpret this
Is the answer:
the SAT goes up by $0.09$
and
the intercept goes down by $0.55$
 A: Airline example. Sometimes there is a direct interpretation of slope and intercept. Several years ago I looked at scheduled flight times (hours) $Y$ and air distance traveled (miles) $X$ for about 100 non-stop flights by a major airline. The regression equation turned out to be $Y =0.646 + 0.00189X.$
The slope can be interpreted to mean than each extra mile increases scheduled flight time an extra 0.00189 hr. The reciprocal is the average flight speed $1/0.00189 = 529.1005$ miles per hour, which is a
reasonable cruising speed for the type of aircraft in use at the time. 
[Notes (1) Actually the air speed is often a little faster for eastbound flights, flying with the jet
stream, and a little slower for westbound flights, but
details of that require introducing a 'direction' variable in the regression equation. (2) There are very brief time periods just after take-off and just before landing during which flights go more slowly. These are too small to take into consideration.]
The y-intercept can be interpreted as the scheduled time on
the ground (leaving the gate and taxiing before takeoff), which
is $0.646(60) = 38.76$ minutes. (Time on the ground at arrival is not an issue because scheduled time is from closure of the gate on departure to touch-down at arrival.)
Your GPA vs. SAT example: In your example with GPA = -0.55 + 0.09 SAT, the interpretation is a little more difficult because there is no such thing as a negative GPA and you have to consider the range of possible scores on the SAT (as @Tinler's Comment notes). 
Often the true regression relationship is a curve.
However, a gentle curve is 'almost' a line if you only
look at it over a small interval. If you have data only in a short x-interval and fit a line that makes sense there, it may make no sense to extend the interpretation beyond the interval. 
In particular, the line may cross the y-axis far above or below $0,$ even though actual (nonlinear) overall relationship between x and Y may
make sense only if $Y-0$ when $x=0.$
For your data, SAT scores lie in the interval $[400,1600].$ so there can be no data beyond that interval, and the heavy part of the regression line
is the only part that corresponds to reality.
One can only say that each extra SAT point correspond
to an increase of  $0.09$ on whatever GPA scale
you are using.

