Answer:
The slope of the line 2x - y = 6 is 2. The slope of a line perpendicular to it is the negative reciprocal of 2, which is -1/2. Using the point-slope formula, the equation of the line that passes through (-8, r) with a slope of -1/2 is y - r = (-1/2)(x + 8). We know that this line also passes through (2,-10), so we can substitute these coordinates into the equation: -10 - r = (-1/2)(2 + 8). Solving for r, we get r = -7.