Sorry if this is too late but, from one of newtons laws we know that: F=ma, so yes one of newton's laws is involved.
This picture makes it clear:
[Image: http://www.physicsclassroom.com/class/vectors/u3l3e9.gif]
Allow me to explain, gravity always acts downwards, so it is represented by the arrow going straight down. We break the arrow into its normal and tangential components relative to the plane, the normal component of gravity is cancelled out by Fnorm, which leaves us with the tangential component of gravity to determine the acceleration of the object.
We can see clearly from the picture that as we increase the slope of the plane, the tangential component of gravity because much greater (or longer if you like), and thus we see the increase in acceleration, again related by the equation F=ma.