Final answer:
Point D) (5, 10) can be added to the grid along with points A) (0, 2), B) (8, 16), and C) (3, 6) to maintain the points as part of a linear function, since it adheres to the same linear equation y = 2x.
Step-by-step explanation:
To determine another point that could be added to the coordinate grid so that the points are all part of a linear function, we need to check whether the given points A) (0, 2), B) (8, 16), and C) (3, 6) lie on the same straight line. This can be confirmed by examining the relationship between their x and y coordinates.
If we observe the given points, we can see that each point follows the pattern where the y-coordinate is equal to 2 times the x-coordinate. This suggests that the points lie on the line represented by the linear equation y = 2x. Therefore, any point that satisfies this equation will also lie on the same line.
By looking at the options, we see that point D) (5, 10) also satisfies this linear equation since 10 = 2 × 5. Hence, the coordinates of the point that we can add are:
- x-coordinate: 5
- y-coordinate: 10
This means that D) (5, 10) is the point that could be added to the set to ensure they all are part of the same linear function.