Final answer:
The slope of the line through the points (-4, 1) and (10, -6) is determined by the change in y over the change in x and is equal to -1/2.
Step-by-step explanation:
The slope of a line that passes through two given points can be determined by using the formula Δy/Δx, which represents the change in y divided by the change in x between the two points. Applying this to the points (-4, 1) and (10, -6), the change in y (rise) is -6 - 1 = -7 and the change in x (run) is 10 - (-4) = 14. So, the slope (m) can be calculated as m = -7/14 which simplifies to m = -1/2.