Question

compare your answer to the model.

yes, it is a direct variation. if the ordered pairs form a direct variation, the rate of change is constant and the ratio of y over x is constant. the rate of change, or constant of variation, is 0.5.

what did your explanation include?

• a reference to the rate of change
• a reference to the ratio of y over x
• the constant of variation as 0.5

Explanation:

Analyze the model response

The model response provided in the image is:
"Yes, it is a direct variation. If the ordered pairs form a direct variation, the rate of change is constant and the ratio of y over x is constant. The rate of change, or constant of variation, is 0.5."

We need to check which of the given checklist items are present in this model response.

Evaluate the first option

The first option is "a reference to the rate of change".
Looking at the model response, it explicitly states: "...the rate of change is constant..." and "The rate of change, or constant of variation, is 0.5."
Therefore, this item is included in the model response.

Evaluate the second option

The second option is "a reference to the ratio of y over x".
Looking at the model response, it explicitly states: "...and the ratio of y over x is constant."
Therefore, this item is included in the model response.

Evaluate the third option

The third option is "the constant of variation as 0.5".
Looking at the model response, it explicitly states: "The rate of change, or constant of variation, is 0.5."
Therefore, this item is included in the model response.

Determine the final selections

Since all three elements are explicitly mentioned in the model response, all three checkboxes should be selected.

Answer:

• [x] a reference to the rate of change (Correct answer)
• [x] a reference to the ratio of y over x (Correct answer)
• [x] the constant of variation as 0.5 (Correct answer)