Final answer:
The slope formula was applied to the given points, resulting in a value for w of -28, which does not match any of the provided answer options, meaning there could be a mistake in the question or answer choices.
Step-by-step explanation:
The question involves finding the value of w when the slope of the line passing through points (-6, w) and (-10, 4) is given as 8. The formula for slope m is m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
Using the coordinates given, the equation for the slope becomes:
8 = (4 - w) / (-10 - (-6))
8 = (4 - w) / (-4)
Multiplying both sides by -4, we get:
-32 = 4 - w
Getting w by itself, we add 4 to both sides:
-32 + 4 = w
w = -28
The value of w is not one of the options provided in the question, indicating a potential error either in the question or in the answer options provided.