Explanation:
ANALYZE
all function graphs are straight lines.
that means that the velocity increases at a constant rate over time.
in formal words : the derivative of a line function (an equation in x of the first order = contains only terms of x with exponent 1 or 0) is always a constant - in fact the slope of the line.
therefore, all these accelerations are constant.
EXPLAIN
as it is clearly visible, and what we all have experienced ourselves when playing with blocks and stuff, or going over slides, or skiing, or ... : the steeper the ramp the faster the acceleration of the object.
the reason is in the size/length of the movement vectors.
going down a ramp the object moves down AND to the side. the bigger the side movement in relation to the down movement, the slower the object moves, and the smaller the acceleration. a straight down "fall" has 0 side movement and so experiences the maximum speed and acceleration.
EVALUATE
as the graphs show, and reasoned by the previous points, the acceleration for angles smaller than 90 degrees is less than the full gravitational acceleration at 90 degrees (free fall).
EXPLAIN second page
the path of a projectile is the sum of the horizontal and the vertical movement.
as with the sliding of objects down a ramp, every movement has a side and a down (or up) movement part.
while the horizontal movement is here considered constant (under ideal conditions), the vertical movement accelerates due to gravity over time, and a prediction needs to combine the information about the starting point, initial velocity and acceleration force (like gravity).
at least based on the information on the paper you are showing.
but I have to point out that depending on what exactly needs to be predicted, usually also the initial angle is needed.
and - also the horizontal movement is not really constant (at least not in Earth), as there is at least friction with the atmosphere, so the projectile usually also negatively accelerates (gets slower) in the horizontal movement over time.
