To find the point-slope equation of a line, we use the formula:
\[ y - y_1 = m(x - x_1) \]
where \( m \) is the slope, and \( (x_1, y_1) \) is a point on the line.
Here, the slope \( m \) is given as 2, and the coordinates of the point are \( (3, 10) \). Substituting these values into the formula gives:
\[ y - 10 = 2(x - 3) \]
Now, let's compare this with the answer choices:
A. \( y = 10 = 2(x- 3) \)
B. \( y + 10 = 2(x + 3) \)
C. \( y + 10 = -2(x= 3) \)
D. \( y - 10 = -2(x - 3) \)
The correct point-slope equation we derived is:
\[ y - 10 = 2(x - 3) \]
However, since none of the options exactly match this format (particularly with the correct sign for the slope), and if we check if any can align with \( y - 10 = 2(x - 3) \):
None of the provided options are correct because option A is incorrect, and options B, C, and D contain errors in both sign and formulation.
Thus, if strictly adhering to the options given, the answer isn't available correctly reflected in any of the choices.
If you want the correct point-slope equation properly expressed based on the values provided, it should be:
**Correct answer**: \( y - 10 = 2(x - 3) \) (which is not listed in the choices).