Explanation:
as you wrote correctly, proportional relationships are in the form
y = mx
that means the line has to go through the origin (0, 0). otherwise it is in the form
y = mx + b
which is still linear but not proportional.
1a.
the rate of change is between 2 points A and B
(Yb - Ya)/(b - a)
in our case e.g. (4, 5.52) and (8, 11.04)
(11.04 - 5.52)/(8 - 4) = 5.52 / 4 = 1.38
when we use other points we get the same result. we see e.g. that when we double x (pounds), then also y (cost) is doubled.
the rate of change is 1.38.
this is also called the slope of the line.
b.
as mentioned in a., when we multiply x by a factor, then y is multiplied by the same factor. it also means that the function contains (0, 0) : for 0 pounds we pay $0.
c.
y = 1.38x
2a.
the slope is (as it is the same as the rate of change) the ratio of (y coordinate change / x coordinate change) when going from one point on the line to another.
we try to find points with integer coordinates to do that.
I see e.g. (3, 4) and (6, 8).
x changes by +3 (from 3 to 6).
y changes by +4 (from 4 to 8).
so, the slope is +4/+3 = 4/3.
b.
the simplest indicator is that the line goes through the origin (0, 0), which it does.
c.
y = (4/3)x