we know that
A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form y/x=k or y=kx
so
we have
a) for x=1 y=0.50--------> y/x=0.50/1------> 0.50
b) for x=2 y=1--------> y/x=1/2-------> 0.50
c) for x=3 y=1.50--------> y/x=1.50/3-----> 0.50
d) for x=5 y=2.50--------> y/x=2.50/5----> 0.50
the value of k is equal to 0.50
so
<span>the relationship forms a direct variation. </span>
the equation is
y=0.50*x
Verify
for x=1
y=0.50*(1)------> y=0.50-----> is correct
for x=2
y=0.50*(2)------> y=1.00-----> is correct
for x=3
y=0.50*(3)------> y=1.50-----> is correct
for x=5
y=0.50*(5)------> y=2.50-----> is correct
Suggest or assume the existence, fact, or truth of something as a basis for reasoning, discussion, or belief.
1. Consider the transformation that maps the graph of the function 
into the graph of the function 
This transmormation has a rule:
(x,y)→(x+2,y)
that is translation 2 units to the right.
2. Consider the transformation that maps the graph of the function 
into the graph of the function 
This transformation has a rule:
(x,y)→(x,y+3)
that is translation 3 units up.
Answer: correct choice is C.
