Final answer:
The slope of the line passing through the points (1,6) and (-6,-3) is calculated using the slope formula, which results in a positive slope of 9/7.
Step-by-step explanation:
To determine the slope of the line passing through the points (1,6) and (-6,-3), we use the slope formula, which is the change in y divided by the change in x (rise over run). Applying the formula:
Slope (m) = (y2 - y1) / (x2 - x1)
Plugging in the coordinates:
Slope (m) = (-3 - 6) / (-6 - 1) = -9 / -7
Therefore, the slope of the line is 9/7. Note that the slope is positive, indicating that the line rises as it moves from left to right.