Final answer:
The correct answer is (c) Inverse Square, Linear, as it correctly represents an inversely proportional relationship and a directly proportional linear relationship, with respective equations being y = k/x and y = kx.
Step-by-step explanation:
The student is asking about the graphical representations of two types of mathematical relationships: an inversely proportional relationship and a directly proportional linear relationship.
An inversely proportional relationship is one where one variable decreases as the other increases, following the equation y = k/x where k is a constant. When graphed, this relationship produces a curve that approaches the axis but never intersects them. As per the options listed, the graph representing an inverse relationship would be of the form (c) inverse square, which is a specific case of inverse proportionality.
For a directly proportional linear relationship, changes in one variable result in proportional changes in the other variable, following the equation y = kx where k is the proportionality constant. The graph of this relationship is a straight line through the origin. Among the options, the linear graph correctly represents this kind of relationship.
Therefore, the correct answer is (c) Inverse Square, Linear, which shows an inversely proportional relationship and a directly proportional linear relationship, in that order.