Final answer:
The slope of the line passing through (-9, -6) and (-5, 4) is calculated as 2.5, which does not match any of the provided answer choices. It appears there may be an error in the question or the answer choices.
Step-by-step explanation:
To find the slope of a line passing through two points, we use the formula slope (m) = (y2 - y1) / (x2 - x1). Given the points (-9, -6) and (-5, 4), we can substitute into the formula:
m = (4 - (-6)) / (-5 - (-9))
m = (4 + 6) / (-5 + 9)
m = 10 / 4
m = 2.5
However, none of the offered answer choices A. 5/7, B. -5/7, C. -2/3, or D. 2/3 are 2.5. There might be an error in either the question or the answer choices provided. If we are to stick to these options, we would conclude that none of them are the correct slope for the line that passes through the points (-9, -6) and (-5, 4).