Final answer:
The graph of a function with points (6, 7) and (10, 13) could be linear if it also contains the point (8, 10), because the slope between any two points is consistent and equals 1.5.
Step-by-step explanation:
The correct statement based on the provided information is that if the graph contains the point (8, 10) then the function could be linear. To determine this, we can use the information from the two given points (6, 7) and (10, 13) to find the slope of the line (if it is indeed linear). The slope (m) is calculated as:
m = (y2 - y1) / (x2 - x1).
Plugging in the given points, we have:
m = (13 - 7) / (10 - 6) = 6 / 4 = 1.5.
The slope is consistent when a function is linear. To see if another point would fit on this line, we need it to form the same slope with one of the given points. The point (8, 10) would create the slope:
m = (10 - 7) / (8 - 6) = 3 / 2 = 1.5.
This is the same slope as before, indicating that the function could be linear. Therefore, the correct answer is D.
In contrast, by applying the same method, you can show that the other points would not yield the same slope, making the function non-linear if any of them were included.