Answer:
The equation 3x + 6y = 10 can be rewritten as:
3x = 10 - 6y
Now, let's consider the possibilities:
A. x-axis only: If x = 0, then the equation becomes 0 = 10 - 6y, which is not possible. Therefore, the graph does not lie on the x-axis only.
B. y-axis only: If y = 0, then the equation becomes 3x = 10, which is valid. So, the graph does lie on the y-axis.
C. Both the axes: If the graph lies on both the x-axis and the y-axis, it would mean that x = 0 and y = 0 satisfy the equation. However, as shown in option A, x = 0 doesn't satisfy the equation, so the graph does not lie on both axes.
D. None of these: Based on our analysis, the graph of the equation 3x + 6y = 10 lies on the y-axis only. Therefore, the correct answer is:
B. y-axis only.