Dilating a line with a scale factor of 2, centered at (3,8), its equation becomes y=3x-4, passing through (3,8) and (6,16). Answer: (B).
When a line undergoes dilation with a scale factor of 2, centered at (3,8), all its points shift to positions twice as distant from this center. Notably, as the center itself lies on the line, it remains invariant through dilation. The preserved slope characteristic of dilation ensures the image line retains a slope of 3. To determine the equation of the transformed line, we consider the original point (3,8) and its dilated counterpart (6,16).
Connecting these points, the line's equation is established as y=3x-4. Therefore, the correct answer to the problem is (B). This step-by-step analysis illuminates how the dilation process, center specification, slope preservation, and point mapping collectively contribute to the derivation of the final linear equation. Option B is the correct choice.