Answer:
- quantities are proportional
- y = 1.3x
Explanation:
Given a table of values (x, y) = {(5, 6.5), (7, 9.1), (9, 11.7)}, you want to know (a) if the quantities are proportional, and (b) the equation for the relation.
Proportion
A proportion is a relation that can be described by the equation ...
y = kx
where k is the constant of proportionality.
(a)
To see if the table describes a proportional relationship, we can compute k for each of the ordered pairs.
k = y/x = 6.5/5 = 9.1/7 = 11.7/9 = 1.3
The value of k is the same for all of the given table values, so ...
the quantities are proportional.
(b)
As we saw above, the equation y = kx can be used with the value k = 1.3 for this relationship:
y = 1.3x